Used to happen to me all the time. In addition, the personal radio station would fetch anywhere from 2-15 songs, then play them in a loop until another fetch request was made. Server-side validation slows everything down. Not the best decision because this really hurts the customer experience.
Try adding a song to a playlist. Can take anywhere from 15 seconds to 15 minutes depending on how much traffic is hitting their server. Not acceptable for a paid service.
Was AM customer for many years, finally decided to stop allowing this service to annoy me so much. Switched to Amazon Music and am quite amazed how much better it is. Its not perfect, but it is zippy fast and has great recommendations. Basically I do not have to "wrestle" with Amazon Music nearly as much as I had to with Apple Music.
Any other music service is likely to serve you better than Apple Music.