From a gameplay perspective, it makes things better at low levels but worse starting at mid levels when monster HD starts outpacing CR (for instance, the Athach, the first MM bruiser, has +8 Str but +10 BAB at CR 8, and that's with 3/4 BAB) and most high-level enemies become full-BAB outsiders and dragons. That can have some bad side effects, like devaluing DR even more and making monsters who rely on more attacks rather than stronger attacks more dangerous.
From a character building perspective, why even have Str at that point? Take Weapon Finesse for Dex to attack, you get BAB to damage, and Str only matters now for encumbrance, Climb, Jump, Swim, and breaking things, all of which basically cease to matter past level 5 or so. Congratulations, Dex is now even more of an awesome stat than before, and people who invest in Str are suckers.
This kind of thing would be great for a fix whose explicit goal was to remove dump stats (ditch Str and Cha, fold their stuff into Con and Wis respectively for a GURPS-ish four-stat system), but just on its own replacing Str to damage with BAB to damage doesn't really work.