I shall broadly put the number of theories that I have come across on the said topic into three categories and I'll call them schools.
1. Scientific (the one proposed by H. Gundert)
2. Imaginative (the one proposed by Bishop Caldwell)
Let us examine each theory briefly.
1. Scientific: H. Gundert proposed that old Malayalam and Tamil were two dialects of a Proto-language.
2. Imaginative: According to Bishop Caldwell Malayalam is a very ancient and much altered off-shoot of Tamil. I believe this theory is the one generally taught to students in Kerala.
3. Ideological: Namboodiri-s sanskritized Tamil and turned it into Malayalam.
Let us discuss each one of them in the reverse order.
This school is not bothered much about doing any research on its own. They borrow theories from either imaginative or scientific school and come out with their own interpretations. In this case, they have borrowed it from Imaginative school. However, even Imaginative school does not say a new language can be constructed by adding words from other languages. It may just say isolation of Proto-Tamils in Kerala region might have give risen to a new language. Languages change drastically with migration.
And I find it hard to believe that foreign word/s in Malayalam instead of being Malayaliized in its morphology and pronunciation can modify the language itself. But though that is a common sense, is not the obvious reason. Addition of Sanskrit words was mere a literary feature and until 19th century a big chunk of the population was hardly literate in any language. (And there are people who believe Malayalam started branching out of Tamil around 9th century CE, which is based on literary evidence. It is absolute foolishness to equate literary beginning to distinct spoken beginning).
I think there must be a study to understand the influence of literary Tamil on spoken Malayalam(even literary) and that makes more sense than talking about Sanskrit influence on spoken Malayalam (also, there must be a study on the influence of Malayalam on literary Tamil, especially on the works produced during Chera period).
Coming to Chera, it is obvious that Chera-s are Tamils considering the literature produced during that time in Kerala. However, probably motivated by this false notion of being lapsed Tamils has led to few historians(Sreedhar Menon/Prof. Elamkulam) in Kerala to argue for absolute Kerala origins of Chera kings (who in my opinion were Munda elites who became Dravidians and created a kingdom with the help of Brahmins). However, I find the so-called the Second Chera empire proposed by Prof. Elamkulam is interesting for some other reason.
I found the following passage in William Logan's "Malabar Manual". It is attribued to some Mr. Ellis.
The Malayalam has not been cultivated as an independent literary language, nor does the Tamil literature, notwithstanding the length of time the country was subject to Kings of Seram(Chera), appear to have been extensively known here, or at least has not survived that dynasty. This is the more extraordinary as some of the earliest and the best of Tamil works were composed in Seram. This remark, however, applies more to Keralam proper(present day north and central Kerala) than to Mushikam or Travancore (present day south Kerala); the residence of Seram viceroys (Logan speculates Peruamals) was in this province, and a knowledge of pure Tamil has always been more prevalent here than in northern districts.
For the remark that Tamil literature didn't survive after Chera-s, Logan makes a point that that was not true and in fact Tamil literature was produced between 10-13th century long after the fall of Chera-s(according to him in 9th century). However, Prof. Elamkulam has unearthed the Second Chera Empire(Kulashekaras of Mahodayapuram) that ruled until 12th century. That probably explains uninterrupted Tamil literature after the fall of the original Chera kingdom. This in my opinion would show there was a difference between the language of the ruling elites to that of common people.
This school though for most part of the things follows scientific methodology cannot control itself from getting influenced by its own unparalleled imagination. George L Hart too is part this school.
One thing I appreciate about Bishop Caldwell's theory is that he considers migration path. I hold on to the view that any linguistic branch must make sense with the migration path taken by people.
According to him, Kerala was inhabited by Proto-Tamil people from the Tamil region. Well, if that is true then indeed there can be no doubt that Malayalis were Tamils once. Unfortunately, he came to the conclusion not based on any physical evidences but just like George L Hart's 'pole' based on couple of words whose etymology he derived with a great imagination. Logan calls this explanation fanciful though ingenious one.
The Malayalam word for east, kizhakku, means beneath, and because melku (west) means above, Dr. Caldwell argues that the Malayalis must have come from the Tamil country east of the ghats, since there they had the low level of the ocean on the east and the high level of the ghat mountains on the west.
Logan tries to match Caldwell's imagination with his own explanation for the terms.
But it is quite reasonable to suppose that the Dravidians, in finding names for east and west, selected words denoting that east was where the sun appeared from below, as it would seem to them, and west as the place where he similarly disappeared from above.
This is the problem I see in studies that run wild in their imagination on semantics. Though Logan makes it clear that he doesn't have any stance on Malayalam being the daughter of Tamil or otherwise, he is attracted towards that argument. Now the whole migration theory (From Tamil region to Kerala) revolves around these words. A situation similar to George L Hart's pole. Where the concept of pllution taboo arising from various factors or regions, just like the migration to Kerala region from regions other than Tamil Nadu, gets overlooked.
By scientific I do not mean correct. I just mean it is at least falsifiable unlike the last one(where you can come out with multiple arguments for kizhakku/melku/pole). I rather think Proto-Tulu-Kannada(or just proto-Kannada) people migrated south at some point of time and gave rise to two new languages(many in fact). One group became isolated in the region of present day Kerala and became Malayalis. I have grown skeptical about the language of Tuluva-s. I believe it may be a mix of SD-I and some other Dravidian linguistic family. I have argued that it must be SD-II but recently I have come across (and old study) that one of the linguists(Shankara Bhat?) observes it has characteristics of North-Dravidian. Therefore, the people who inhabited Kerala region may have been culturally Proto-Tuluva-s but not necessarily linguistically proto-Tuluva-s.
However, as required by linguistics, two languages are considered separate languages if they are either;
1. mutually unintelligible
2. intelligible only one way (Danes understand Swedish but not the other way round or is it vice versa?).
But political definition of an independent language may differ. In China, there are eight languages that are mutually unintelligible. Though by linguistics, those are eight independent languages for the people themselves those are eight dialects of a single language.
With these definition I believe Malayalam spoken by people in Kasaragod must be considered a separate language in view of the fact that central/south people would find it difficult to comprehend.
It is tough to say Dravidians are the first people to colonize south India. It is also difficult to say whether the Dravidian language is the first one to be spoken in that region. It is possible that Dravidians as we know them today by their certain cultural markings came later and picked up the existing Dravidian language spoken by earlier migrants. By genetics, as far as I can see, the previous population was certainly not Munda in South India. It can be Vedda, however, any distinct language that the Vedda might have spoken doesn't exist anymore. Also, the genetic profile of Vedda is not available.
1. Malabar Manual, William Logan
2. Linguistics, MIT Press Publication
3. A Survey of Kerala History, Sreedhara Menon
4. The Dravidian Languages, Bhadriraju Krishnamurti