There's feels like there are a ton of issues here being rolled into one problem with stat point allocation, and to assume that this problem never really occurred to WotC during the bazillion playtests they must've had, feels a little like missing the point.
If players are desperate for HP because they feel too squishy, it's because the games they play are too combat focused, where HP balance is paramount. The rules of Bounded accuracy are explicitly intended that, in non life-or-death circumstances, a level 7 character does not feel useless if they're with a party of level 12's. The main difference is HP, and if your combats aren't all semi-lethal, meh, you can get away with it. If, however, there's plenty of intrigue, puzzles, and social interaction, then you're going to want to have at least 2 good INT, WIS, or CHA, or adequate.
Second point is the character creation itself - as someone mentioned above, rolled stats solve a lot of problems with choice. Speak to your players and rather than have them bring a character concept to the table before hand ("I want to play a Monk today, dude I'm really psyched!", "Well come in off the porch and we'll talk"). Rolled stats, character background, THEN choose a class. Alternatively, once the point buy is done, ask each player why their stats are like they are - poor justification leads to an immediate deduction of 2 from the stat. The wizard with 14 CON is going to have to come up with some pretty wacky




to justify being as physically hardy as the Ranger with 14 CON.
Thirdly, Maybe explain to your players that the difference between 10 Con and 14 CON is largely negligible - at 5th level, that's 10HP, have a better DEX or WIS save is just as likely to save you those 10HP (Maybe not mathematically exact, but close enough), and they aren't there to be hit anyway. HP, AC, and good saves all block damage in different ways - yes HP feels more reliable, but constantly fluffling WIS and CHA saves is fricking annoying.
Fouthly, CON is not a story skill (none of the physical stats are
really, in most cases), and D&D is generally speaking about player stories, and about the story of the world itself. The more people focus on this, and the more they know the game will focus on this (I want to play a social polymath, but I'm worried the DM will keep trying to kill me with monsters) I suspect the more people treat CON as a nice-to-have option. If that isn't the game you want to play, and you do want a dungeon crawl hack-n-slash, CON is going to be the cleverest option.
Lastly. If you're still reallllllllly set on nerfing con. THen as someone mention above, MAX the HP dice per level and remove the CON bonus (except for racial perks that get +1 because that's their thing) - but leave CON with healing and everything else. Ergo, high CON scores recover quicker, but HP is more aligned to class.