I think what you may not be seeing is that you'll be missing out on a lot of flavour too. Having seen a monk in action I feel like the highlights of the class are:
- Having enough movement speed and wall-running to move anywhere you want as you please
- A million lightning-fast punches and jabs per turn
- Face off against a dragon in your undergarments because weapons and armor are for dummies
- Sprint to the enemy mage hiding in the backline, punch them three times, stun them for a round and sprint back to your party like it's nothing
- Edit: Almost forgot - leaping down a 100-foot chasm without feather fall or running up a 50-foot tall wall and then jumping down on the other side because you can
By building around Strength, heavy armour and shields, you will be missing out on ALL of the above. Maybe that's fine if you're okay with that, but you won't have the true 'monk experience' imo.