Instead, you need to have either a stat boosting job or a stat boosting esper equipped, and this is tedious when you have to swap them in and out after every level to guide the stats the way you want.
That's called "customization." You can build them up as you see fit.
Has anyone ever written a hack that will increase each stat by a few points after levelling up?
A few points?! Well, it makes little difference in FF6 since both damage formulas use level as the majority factor for damage. But in FF5 that would make a bigger difference since that formula seems to be sane.
To actually answer the question, no I don't believe so. Nobody has hacked FF5 (except for the translators) and I'm almost 100% certain that nobody has made such a patch for FF6.