As soon as the commander is exiled it should prompt the controlling player to place it in the command zone. Seems more like a bug than the card working as intended. All other "exile then return" effects I've seen prompt the controller to do so.

Yea this is just a wildly unfun card.
The same reason you seemed to ban Drannith Magistrate or Pithing Needle, is the same reason you should ban this card.
I suppose the cards I listed can be preemptively played and Housemeld is a reactive sorcery is the argument? That would be a poor argument because there are more efficient cards like Witness Protection that do what Housemeld intends without shutting the door on you EVER getting your commander back without enchantment removal.
It's not fun for your deck to just lose to a 4 mana sorcery.

Housemeld is, by a wide margin, the most toxic card ever designed for brawl. It was clearly designed by someone who frankly doesn't understand the entire core premise of command zone based formats. It's akin to printing a card into Modern that prevents players from side boarding between games, or reprinting all the best cards in modern into Standard. It's antithetical to the format and an absolute feel bad every single time it's cast. It should be banned, frankly it should never have been printed.

I scope every game I see it cast in and it's easily the worst taste in my mouth when playing Arena. I wish I could tell when it was in someone's decklist at start so I could just scope before the mull. I hate it that much.

An easy solution would be changing Housemeld into a "slow flicker" (the ones that return the card at a later time instead of immediately). It would barely change the card and make it more fair in Commander-adjacent formats.

I wouldn't hold up much hope for them changing it since they don't seem to give a **** about proper balancing of Brawl, banning stuff like Drannith Magistrate (which every deck should be able to remove), but allowing stuff like Mana Drain and all the busted Alchemy cards to warp the format...

It's all one effect so you can't put your commander in the command zone. The only time you could is if the card fully resolved and your commander went to exile/graveyard.

Housemeld currently still doesn't allow a response to move your commander to the command zone despite moving zones during the effect. Is this working as intended or a bugged interaction?

the effect should be changed. at the time of typing this it looks like the attached picture/