The iTunes remote app is suffering from long-term neglect, and appears to have been deprecated, probably because no one much in Apple corporate feels the need to use it. For those of us who like what it does (or, increasingly, what it used to do) this is hugely disappointing.
Along with other respondents here, I like to pipe music around the house from a static Mac that hosts my entire music library, stored on a local drive. This is a far better option than AirPlaying it from my phone and having the music interrupted by calls, text message alerts, random system noises and connectivity issues. It can be a brilliant way to wrangle your music collection, but the ongoing neglect is destroying its usefulness.
An iPad Mini on a little stand running the Remote app is how I liked to control things, but the iPadOS implementation of the app has suffered even worse than the iPhone version. In addition to the problems listed by other contributors here, there’s no PLAY control when you line up an album or playlist on the iPad, so it’s shuffle or nothing because you can’t manually add anything to Up Next. It’s a depressing shambles and I urge anyone reading this to complain bitterly about it on Apple Feedback. It might not stop the rot, but at least you’ll have had your say.