As long as bonuses can stack at all, bonuses only stop mattering if against every conceivable monster you attack (under every conceivable situation) you need only a 1 to hit - And if every conceivable monster can be slewn with one strike. Just to state the extreme. Of course there is a cut-off point where it doesn't really matter, but that point is pretty far off in D&D.
I'm not saying the bonuses
stop mattering, just that as play progresses, the amount of your bonuses from stats decreases in importance relative to your other bonuses. If your PC has, say...+6 from strength, +4 from a weapon, +15 from his level and +5 in other bonuses, that strength bonus is 20% of his total bonuses.
Even assuming that initial stat roll was 4 points higher than the next best front line combatant, it provided an average of +2 better than that other PC. That seems huge at low levels. But if that PC paced him for Str and other bonuses as they leveled up, that's only a 6.7% difference in probabilities from one PC to another at the end. That's
not a huge advantage over time.
And if you factor in the vast panoply of Str or combat boosts out there- the Kensai's +8 Str boost, Rage, Righteous Might, the Expansion psionic power, etc.- that +2 bonus derived from a better starting Str is almost miniscule.
(Unless AD&D and OD&D were very different).
They were- in older editions, Str didn't have a linear bonus progression. The difference between Str 17 and Str 18 wasn't so bad, but there was that bizzare stretch between 18 and 19 with the "/" mods... An 18/01 was RADICALLY weaker than an 18/99 or 18/00 in terms of damage output. On the upper end, you could 1-shot critters even at 1st level.
There were also far fewer opportunities to boost Str and other combat mods than in 3Ed/3.5Ed/4Ed- and NONE were level related.
IOW, in those days, there was no real disappearance of the importance of a really high Str.