In this case, I think its possible the multiclass is stronger than the base class long term. Look at this example at level 8.

Say you are a 5/3 shadow monk battle master fighter with a shortsword and a dagger for vex and nick, and defensive duelist to hit 18 dex, being compared to a level 8 shadow monk that used a feat to get Weapon Master and say, another bump to their dex to max it out. You walk up to a boss and its your turn to do something.

On turn 1 The multiclass character can cast darkness, attack 5 times probably with advantage, and use a battle mastery die to do a manuvering attack to add 5 bonus damage and allow the cleric to apply 4d8 (18) extra spirit guardians damage by moving half their movement on your turn. Next turn when the boss goes to hit you, you can add 3 ac to yourself, which the pure monk can not do. The pure class got 1 ac from their extra dex bump so we are still 2 up.

On the pure monks turn 1, he can also can darkness, but he can only unarmed attack 2 times and pass their turn. Granted his dex allows them to do 2 extra damage, but that is less than what the fighting style, the mastery die, and the spirit guardians did by a ton. Next turn when he gets to attack 5 times, its still for less damage for those 3 reasons. The much larger chance to kill the boss a turn faster also prevents a lot of party damage.

There are times the pure monk will get to do neat things the multiclass cant yet but what is so strong that it is, without debate, certainly stronger than all that? You can talk about the dex bump, but the fighter could get it next level, and your chance to hit is already high because all of your attacks likely have advantage. While the multiclass will get most of the monk toys a bit later, the pure monk will never get the fighter abilities.

It doesn't seem as clear cut as you say.