Well certainly there are drawbacks of using thousands of variables in a form post. Performance will drop on both sides, server and client. All values are encoded, copied and decoded several times, so this eats up performance and memory. And what for?
But I'd say that this is not really the point. The thing you should give some thought is this: why the heck does that stuff required thousands of variables in a post? That sounds insane. I suggest you should rethink the architecture behind that. There should be a much easier and more robust solution. A typical approach would be to encode all those variables in a single one, typically some JSON data block.
So far I have seen only one example of an architecture where someone tried to implement a csv file editor as a single html/http based form, posting all fields as separate variables. Believe me, there are better approaches for this.