You can see growth points somewhat, but yeah, seeing where those points went exactly would be beneficial. As of right now, it's really just a guessing game unless you have a unit with stats in the opposite offensive stat (so if you see a spearman with like 3 mind at level 1, that one has points into mind for some stupid reason).

As for personality and background, that's probably asking for too much. There are some personality traits you'd avoid at all costs, and some you'd go out of your way for. Some backgrounds are also really strong (like blacksmith, doctor, story teller, etc). It's probably best if that remains random. Besides, you can create custom characters with whatever you like.

I feel that seeing all the hidden information behind a character at recruitment defeats one of the points of the game. It's much more interesting to watch how a character unfolds and take advantage of the cards you were dealt with rather than getting a sneak peak into every character you recruit and getting all of a character's info for free.

I think Devil_JCS and Vatn have the right of it: learning about your characters is a huge amount of the fun! That said, there are "tells" that can help you guess a character's personality right out of the gate: different personality types have different default facial expressions, and some of them alter a character's base stats in ways that aren't likely to happen otherwise. (For instance: if you see a Psy Healer with a counterattack limit of 1 and an angry expression on her face, she's probably Vindictive.)

You can oftentimes deduce a character's growths from their stats (especially if you're recruiting them at level 1), as growths tend to impact starting stats in a very direct way. (A swordsman with 3 base strength at level 1, for instance, has a base strength growth of 3.)

I'll concede that personality and background are fine hidden but something to quickly identify where the growth points are (Stars next to the stat during recruitment maybe?) just helps so you don't have to snoop on every single character. Just a suggestion, you make the game however you envision it, i'll continue to enjoy it regardless.