Yet with the standard array (as a PC proficient in heavy armor), I can dump Dex, Intelligence and Charisma, and have a good Strength and Con and a reasonable Wisdom.
Indeed, but your Initiative and ranged attacks - both important capabilities - will suffer for it.
I already specified outside of two-handed weapon builds (although good point about grapple/shove builds) you give up much
less if you dump Str and boost Dex rather than vice versa. Most groups I've seen don't seem to bother with encumbrance, so the only thing you lose out on is the ability to initiate shoves and grapples.
Strength based builds are also disproportionately reliant on feats to complete them.
Heavy armor and Dex 8 gives me a better AC than even a PC with a Dex of 20, and all from a lower level.
Polearms and Great weapons (two very popular fighting styles rely on Strength) cant use Dex at all. Shield master - which is the cornerstone of any S+B build - relies on an Athletics check (so again, strength is go-to). Grappling, shoving etc all rely on Athletics (as do most of the optional combat manouvers as well).
Barbarians are forced into Strength builds as well; as is any Paladin MC combo (requiring at least a 13 Strength).
The issue isn't that Strength (and Intelligence) -based characters are not viable. Its that Str and Int are generally either primary or dump stats, with little in between. Whereas Dex is useful for any character and so is primary or secondary, and dumping it has significant downsides for almost any character.
Barbarians might be "forced" into Strength builds, but Dex still provides significant benefits.
Barbarian and Paladin MC combos require 13 Str, but Monk, Rogue and Ranger MC combos require 13 Dex.
Personally what I'd like to see is
both Str and Dex being useful for any martial character, rather than being able to dump Str with few repercussions for many warriors. That has additional stat balance and bounded accuracy implications however.