I suppose you could wing it if people are sufficiently musically talented or have a lot of exposure to musicals, but I would think it would tend to be a train wreck in terms of actual game fun for everyone involved lol
I think you and some others are effectively confusing LARPing and TT RPGs. This thread is about TT RPGs.
In TT RPGs you don't generally break into actual song when your Bard or whoever sings a song. Most groups don't RP literally every single sentence of every discussion or negotiation - indeed, my experience is that the majority of stuff you could potentially RP out isn't.
Why would it be different with musicals? Musicals are still a genre, and that genre has its own rules and tropes and so on, even if you have to be pretty into musicals to realize that.
So the real question is, would a "musical" genre TT RPG be about making a musical, and the tropes around that, or would it be about being a world governed by the rules of a musical? I think the latter seems more like as a TT RPG concept, and we've seen it done on TV before - in that case, it's very much about following the structure and concepts of a musical, and looking at what conflicts would be and how they'd be resolved and so on.
It would take someone extremely familiar with a wide variety of musicals to design such an RPG, and I wouldn't be the person to do it, but I'm pretty confident it could be done, and you could mimic the genre and the vibe pretty well. The singing? Not so much but that's like saying you can't do an action movie well because you can't see the action - I think people would be able to imagine it.
So you wouldn't need musical talent, and the players wouldn't necessarily need "exposure to musicals" any more than D&D players need "exposure to generic high fantasy", if they could parse the rules, setting, etc. - which is to say it's beneficial, but not vital. Nobody would need to make up entire songs at the table, you'd just want to be able to make up what your character was singing about and so on.
I think if you designed the structure right, it could be a lot of fun.