Why stats should cap at 30

Counterpoint:  Caps of 20 do solve the problem of single-stat focusing being stronger, but it also removes almost all effect of _any_ stat building at all.  Your starting array now becomes the majority of your progress, and for at least one stat (or more, depending on racials), you start out halfway to the cap and everything else is just a barely-relevant +5% every couple levels.  You can choose whatever you like because the only important choice was something you already made at level 1, when you decided on your starting array and your racial buffs.  A metaphor I used elsewhere was that of using a steamroller to flatten a molehill, and also destroying the rest of a garden as collateral damage.  A more extreme example would be my 10s across the board, or mods ranging from 1-3 but also rolling 1d100 instead of 1d20.  You still get your "freedom" to choose your mods, but it will often be outweighed by the sheer size of the die being rolled beside it.  That 1d20 doesn't change, it just makes your build and your decisions matter less compared to how lucky you happen to get, which is a ridiculous thing to encourage unless we're trying to remove builds entirely.  The assumption I'm making is that people will put their highest starting stat as their main one, and there will be no "branching out" because an extra 5% to succeed is almost an empty level if left on its own.  My "mandating" at least a 20 comes from the fact that even the least optimized example character used had one, but an 18 or even a 16 in it would be nearly as viable, since that's only a 5-10% loss in accuracy compared to their stat-pumping companions, alongside damage loss, but in exchange for building in some new direction that they chose to.  In my ideal world, ASIs would come often enough that reaching 20 in one stat would be a simple thing to achieve, and everything after that is hardly essential to combat effectiveness.  As I said earlier, opposed checks such as grappling with Basilisks would be keyed near that 20, giving people who build it a strong advantage and those who dump the stat a signifigant disadvantage that still isn't automatically lethal.  Note that even a -1 mod compared to a Basilisk using +5 has a not-insignificant chance of escaping.  Meanwhile if Basilisks were set near the "middle of the road" for a cap of 20, a mod of -1 compared to a mod of 2/3 would be almost meaningless, since there are only a few results on the d20 that would cause either mod to be the reason that opposed roll was lost.  Similarly, a player who is as strong as possible, with a mod of +5, is also easily grappled by some random snake thing that he stopped caring about a dozen levels ago
And let the record show that, powergamer as I am, I would not be building to 30 in most situations under this increased cap