I would recommend looking hard into Firebase for this project, especially if you do not have dedicated full-stack or backend members on your team.
The real time database, as you mentioned, is a great option, but I would also look into Firestore. Similar to RTDB, it adds more functions and some cool methods as well. Also, another great thing about Firebase is you have easy access to storage and dead simple auth as well.
Node.js Express MongoDB Socket.IO and Apollo are great technologies as well, and may be the better option if you do not wish to cede as much control to third parties in your application.
Overall, I say if you wish to focus more time developing your React application instead of other parts of your stack, Firebase is a great way to do that.
I totally agree with you.
The only issue is most features of firebase are paid (and from my perspective costly) which could be a concern when the app grows and they might need to migrate which would be a lot of work.
But if it's only a prototyping then it's all good.
I hear you. I honestly haven't looked into hosting costs of Firebase vs Express/Mongo much.