Healing in 5E has gone way overboard into redundancy.
1. At one point in the rules it mentions that characters get all lost hit-points back after a long rest (at least 8 hours), along with half of the spent healing hit-dice.
2. During a short rest characters can roll hit-dice to recover hit-points, potentially returning to full.
3. There is a healing kit available in the equipment that has 10 uses and can help restore hit-points.
4. Clerics can use a number of spells to heal characters, including some at-range.
5. There are healing potions and likely other magic items for healing.
6. Some classes even have their own healing capabilities. The fighter has an increasing number of Second-Winds that allow a die to be rolled to heal some hit-points (up to 10 + CON modifier) and this ability recharges between short or long rests. And at 18th level the fighter even gains a minor form of regeneration.
I see no real issue with numbers 3, 4, and 5. Numbers 1, 2, and 6, should have been options, not Basic game inclusions.
Getting back to the Ability score increases. Some classes have more levels at which they are able to do this than others. Once we see the monsters we should be able to determine if this is baked into the core system math and then we need to determine how to remove it. It should not be core, it should be optional since something like this is much easier to add than subtract from the system.
I like the playability of 5E, but I keep finding stuff that should not be part of a basic game.