Not if you have a single flying thing to get at, no. But you can throw them (with the attack action) move and punch or flurry something else.
How is it any different to Barbs and Paladins? They also suck at ranged combat.
Not that it's really much of a concern. Any Monk worth his salt is decked out in Boots of Flying by mid tier at some point. As should any Barbarian or Paladin (two other classes that suck with Ranged attacks).
Personally I give all Monks a Flying speed for a round (equal to land speed) when they use their Step of the Wind class feature from 14th level onwards.
Thats just my HR though.
Even then, it's good to have a way to bring flying enemies down for the aforementioned paladins and barbarians.
Relying on magic items isn't something to build around, either. Choosing monk shouldn't force the DM to introduce a flying magic item, especially if they could've flown in a different archetype.
Speaking of paladins, did you know you can crit fish Fire Snakes like a paladin can with spellslots? And since it isn't a spell, you can dump all your ki points at once. For example, at level 6, you can crit fish and do (2d6+dex+8d10) fire damage in one attack, deciding to upKi after the attack hits, of course and assuming you wanted to flurry of blows to fish (which you didn't need to do, at this point you make 3 free attacks a turn, an extra attack for extra 2d10 might be worth it).
They certainly aren't just a one-trick pony as you imagine, though. Dragging flying enemies down is their strongest card, yes, but they have hard hitting AoE's unlike other melee combatants. These AoE's usually outdamage flurry of blows per Ki point so they're a great option to
really put numbers on the board.
Of course, EK's have a melee/AoE system going, but they don't have evasion, proficiency in all saves with potential to reroll, BA dodge/hide/disengage, unarmored movement, and Stunning Strike all at once like a monk does.
This is why I discourage comparing one feature of a subclass with another feature of a different subclass, they have different synergies with the overall class.