Since the game just recently got released, I'm sure at least a patch or two will be released by Square Enix.

In this case, I would instead create a support issue within the game's forum, so that the issue can be fixed, rather than using a mod as a workaround. Otherwise, SE may never realize that it is a problem that needs fixing.

Because they dont look at feedback. Im pretty sure creating a issue wont work on them either.

They have to start caring about titles first, which is not their history.
They care about money

I don't think Square will ever see this as an issue. For them, some input lag is not a game breaking bug and therefore has very low priority.

Regardless of personal opinions, if you look at their track record, they've released at least one patch for almost every game. This means, that the most crictical issues (where people complain the most), will be the things that they will generally focus on for the first patch.

Modding something like this does not make sense until we can tell that they aren't working on fixes. Wouldn't you rather trying getting this into the game's code, rather than forcing every user to download a mod?

Well yes, only the most critical issues will be fixed, and as far as I can tell, very few are complaining about the input lag issue. It's mostly the tablet UI that gamers want fixed.

I may be wrong and they fix this tomorrow, which would be great. But either way, I'll leave this request here in case it never happens.