As the title suggest to increase the player hit-point per player level. Here are a few reasons why, 1) it would make the game more immersive and would make levels more more meaningful, 2) so you don't get two-hitted by creatures, and 3) so you don't have to retreat back and bandage up every 2 seconds while in the middle of a fight. An example: For each level you get 50 points of hp so by the time your level 25 you will have your default which is 500 hp plus 1250 hp which equals 1750 hp in all.
Yes, seconded. That way you could also "stretch out" the difficulty levels of the POIs so they'd better match with the character level progression. It would also allow you to introduce tougher mobs in appropriate places. Or, if you want to do the perk/skill/whatever system instead of level progression then do remember to have "health" as one of the choices where you can then pour your points if you so wish.