First of all, that's a little insulting. I actually have thought about it. And there is literally nothing so iconic about it that I can think of that isn't covered by fighter/monk/Tavern Brawler that it deserves a full class, as far as I can see.
I mean, if your criteria is "I can think of some stuff you could do with it", you can justify literally anything as a base class. I think that the criteria should be much stricter than that. I'm open to the idea that a brawler (for instance) might meet those criteria, but I have seen literally nothing to back that up, despite asking several times in this thread.
Except that those classes are already in the PH. Sure, you could design a brawler that fills the same design space as the monk. But why? It's redundant; it doesn't fill a design space that needs to be filled. I mean, you could design a swordsman, axeman, hammerer, mace-man, and flailer class, but none of them are likely to come out as anything more than variant versions of the fighter.
Again- what's missing?
To justify a base class, I think you need to be filling an archetype that isn't already served. Brawler doesn't, as far as I can see. Arguing that the monk is similarly unjustified misses the point that the monk is already in the PH; that the monk (and other unarmed options) are the reason that the brawler isn't necessary. Take the monk out, and sure, there's room for a brawler... but the monk is already there. It's the existing work that fills the slot that a brawler might otherwise fill.
Again, I am open to the notion that there's something there the monk isn't doing. But I'd need to see some kind of evidence to back that up. So far, the argument seems to be, "But I can think of stuff it could do," which isn't nearly enough to rise to the standard I would use to evaluate whether a base class is justified.