That's kind of true, but not as much as people tend to think, because cantrips other than Booming/Greenflame Blade and Agonizing Eldritch Blast don't get ability score modifiers, and even Booming/Greenflame Blade only get them once. A Str 16 Valor Bard who takes e.g. the Mounted Combatant feat and uses a lance will be doing 2 * (d12 + 3) = 19 points of damage by 6th level, and even if he learns Booming Blade at 10th level, he'd still only do (d12 + d8 + 3) = 14 points of damage with it at 10th level, (d12 + 2d8 + 3) = 18.5 points of damage with it at 11th-16th level, and (d12 + 3d8 + 3) = 23 points of damage with it at 17th-20th level. (Mounted Combatant isn't even strictly necessary, but it's convenient for keeping your mount alive and has other benefits and I quite like it, so I cite it in this example as a viable path that a Valor Bard could take. But you could also rely on Phantom Steed, or Find Steed, or just use kiting tactics and have a string of backup horses waiting nearby just in case.)
So in practice, all Valor Bards will do cantrip-competitive weapon damage even without maxing their attack stat, for as long as the game is likely to last.
Edit: or you could use a greatsword instead of a lance. Blind spot on my part--I like sword-and-shield for Valor Bards and sometimes forget that greatswords are an option for them.