The first problem is that of the failure of NMG analyses to describe the actual distribution of case morphemes, since in almost any stage of the language that one might want to examine there are a number of situations where case morphemes are in fact replaced by postpositions, or there is variation between the occurrence of one or another case ending, and/or one or another of the morphemes usually called postpositions. For example, NMG analyses fail to assign an appropriate separate place in the system for instrumental and sociative uses of the so-called third case (the third case in fact has separate suffixes for instrumental and sociative uses, but is still regarded as one case). NMG analyses also include an ablative case that is clearly formed from a locative case-marker (-il) plus a postposition (-iruntu). (In modern spoken Tamil, the system breaks down even further, with postpositional morphs completely replacing case suffixes in some instances, or combining with case suffixes to form what seem to be as genuine a kind of `case' suffix as is the ablative, which was long ago admitted to membership, despite its clear construction using a locative marker plus a postposition.)
NMG's also typically fail to provide an adequate explanation for the genitive, which often precedes other case markers (i.e. has other case markers suffixed to it) so that it is then relegated to the status of an `oblique' form, or is classified as an `adjectival' form, or a stem alternate; in any event it is demoted to something less than a `real' case marker, ostensibly because of some notion that a `true' case marker in Tamil could not have another genuine case marker affixed to it.
This ambiguity of the status of the genitive is not so much of a problem when it comes to nouns, but with pronouns, where the oblique stem may function as a genitive, e.g. en pustakam `my book' one might wonder why this oblique stem can be genitive when case markers can be added to it that also function as genitive, e.g. ennutaiya pustakam (spoken ennode pustakam).
In the modern spoken language various changes have also led to some homonymy in the system, with the Literary Tamil (henceforth LT) genitive form udaiya being pronounced in Spoken Tamil (ST) sometimes as oode, in other dialects as oodu, which is homophonous with the `sociative' udan/oodu/oode in some dialects; in others no such confusion may result, or some other morpheme may be used for `association', such as a postposition, e.g. kuuda, toneyle or some others. The instrumental case marker itself (LT -aal, ST -aale) may also vary in ST, with some dialects employing postpositions instead of the official instrumental ending (LT kaiyaal).
Lest it appear that I am trying to build up suspense about the origins of this confusing system, only to show my great erudition when I reveal the true system, I should say that it has always been obvious that much of the case system has been modeled on that of another language, and that the natural system of Tamil has been forced into this other mold, with the result that what are clearly two different cases are made to fit into one because of some notion that the system had to have seven and only seven cases.
To Indo-Aryanists it will be obvious that much of the above NMG system is modeled on the case system of Sanskrit, which has seven or eight cases (ablative and genitive are often subsumed under one, vocative and nominative under another, etc., depending on the paradigm of the declension in question). Even the order of Tamil cases is approximately the same as those given for Sanskrit. Since this system does not, as we have just seen, work very well, and is obviously a model imposed from another language, (just as Latin was once used as a grammatical model for modern European languages), it is obviously high time to abandon this foreign system. Since Tamil grammarians usually abjure any influence from or debt to `northern' grammatical models, there should be no difficulty in forsaking this inappropriate grammatical model in favor of one designed to fit the facts of the language.
In fact when we look at the history of grammatical treatments of Tamil from the oldest records onward for an idea of what the case system was originally like, and how it has changed, we see that there has often been disagreement about how to analyze the system, and that there has also been a constant history of substitution of new morphemes for case endings, replacing older morphemes previously in use. What has not happened is a reinterpretation of the system to include new categories, or new cases, as well as the new morphemes. And of course when we get to the modern language, there is very little attempt by any grammarians to deal with the system at all, since the Spoken language does not officially exist.