For me, I think dump stats shouldn't exist. Dump STR should be heavily penalize, but so should dumping INT, WIS, CON, DEX, and CHA. Dumping any ability score should hurt.
So the problem isn't that boosting STR isn't valuable, but in many cases dumping it is too easy, just like most other ability scores.
The problem I see here is: if no stat is dumpable, everyone needs to be good at everything - which requires flat arrays. If everyone is going to have a +2 mod in all the abilities anyway, because anything else will be punished, why even have ability scores? Why not just assumes a flat array and give everyone a +2 to everything (or reduce the dc's)?
Not that that's a bad option - it has a lot going for it, but only going halfway by making everyone need a minimum of 12 in everything is removing real choice without reducing complexity. Go all in. Remove ability scores entirely and just use proficiency.
The other direction to go would be to open up more dump stats - make it so players don't feel like their character will be useless or too fragile or whatever if they decide to be clumsy or sickly. I find the lack of variety comes from the fact that most classes go a long way to defining what your ability scores will be because the usefulness is so lopsided. If you're playing a paladin, you tend to play the same ability scores because anything else will be a significant hindrance.
The three stats I almost never see dumped are dexterity, constitution, and wisdom. The others are often dumped for pc's who don't use them to attack, but these three can feel necessary for everyone. Add in a primary ability score for attack rolls, and you get a choice of two places to put your low number.
For Dex, I think this just means more way to get a decent (not necessarily great, but good enough) AC without using Dex for classes that don't get heavy armor. I'd suggest making medium armor either a flat AC like heavy armor or let it use either str or dex, and making the
mage armor spell set a static AC (I'm thinking 15), regardless of ability scores. Now dex for AC is only a must for rogues and some bards, who were probably going to have a high Dex anyways. (I'd probably let bards take mage armor, though.)
Wisdom is fairly dumpable already, (you really only need one person in the party with good perception) but letting Inspiration be used to reroll saving throws would probably help.
Con is a tougher nut to crack - if you remove Con from hit points, it goes from 'necessary' to 'nearly useless', but obviously it's too important (outside of saves, even) to be dumped under the current system. So you'd need to lessen the impact on hp without removing it. My current thinking is to make to add you Con score (the 3-18 number) to your hp once. This also helps with low-level squishiness, but I don't know if it will really work. This needs playtesting.