You just said, "Strength is not what I would consider a dump stat."
I'd argue that "number of builds" is a false metric, and not just for this particular subject either. Any given character has exactly one build. It doesn't matter how many other people need Strength when the salient fact is that you don't. And having some characters value some ability scores more highly than others isn't exactly a sign of imbalance, in any case.
You just said that Str and Int are comparable in a lore bard. I'd go further and contend that they're not comparable at all: I would have been very foolish to play this character with 16 Str and 8 Int, because I get far more benefit from making frequent knowledge checks than I do from rolling almost nonexistent melee attacks. (I should add that we both have a wizard and use the alternate encumbrance rules.)
If players are metagaming around their characters' low Int scores, that's a table problem that goes beyond the balance of the ability score rules. And setting metagaming aside, low Str is far easier to play around -- see again the aforementioned bag of holding/mule. As far as DM operation goes, being strict about the encumbrance rules is "operating a certain way" -- lots of DMs don't, and the rules themselves are written to make them easy to handwave. What's more, you just highlighted the alternate encumbrance rules, which is definitely "operating a certain way".