I'm playing a monk in a campaign right now so I'm sure as hell biased, but there's a couple of things I would love to do with my STR 10 monk that'd make him feel super cool.
1) give monks at a certain level (maybe 2) the ability to use DEX acrobatics to grapple and push enemies. Maybe I've watched too many kung fu movies, but this is monk essence in my mind. Monks get a number of attacks and this would be a cool way for them to use one or two up. I envisage tripping two enemies followed up by a flurry when they're down. Cool.
2) also be able to use dex acrobatics to climb and jump long distances. Again too many kung fu movies.
Yes there will be naysayers who claim that I should just pump my strength and choose athletics as a proficency, but it's very limiting and I can't choose other important proficiencies like nature and medicine. You wouldn't put your cat in a box would you? You wouldn't do the same to my poor monk, would you?
No, I say freedom to monks! Make them the zany martial class for people who like fun!