I was talking with a friend the other day (also a DM) about house rules. He said that he does hit points like this:
1. Starting hit points = your CON score.
2. Hit points per level = 1 + CON mod (min. 1).
3. Toughness feat = +1 hp per level.
4. Favored Class = +1 hp per level.
It's not necessarily my cup of tea, but it works for him and his gaming group. Maybe this is something worth considering in 5E.
Some of these DMs like really weak PCs. I gaurantee you he is not adjusting his monsters downward.
That said, I do think particularly in 3e, some of these monsters had way too few HPs and in 4e many of the solos had way too many.
For PCs, it is kind of a sweet spot. I do not want the 2e thing where a wizard could get two shot by a house cat. But, you probably should not have men and orcs with the hit points of a dragon the size of a building either.
I have always thought HP should be by size as well as level.