WiFi login at my gym requires entering my email address, but Watch series 4 does not support it?

It seems that any WiFi that initially asks you to simply "accept terms and conditions", or "enter your email address", etc, will not work on Apple Watch (non-cellular Series 4). I learned this AFTER I signed up for Apple Music service. Every PlanetFitness gym I go to requires you to enter email to join WiFi. And Golds requires "accept terms and conditions" checkbox. I really wanted to stream Apple Music to my watch while working out, leaving my phone in the locker room. This is a disappointment considering the cost of Apple Watch and the cost of Apple Music subscription, and the fact that most public WiFi networks are captive, and require some kind of web screen to use their WiFi.

Will there ever be a Watch OS update for Series 4 that will address this simple connectivity issue?

I have already sent a suggestion to the gyms to remove the login screen, but I doubt that will change anytime soon.

I already have music playlists in the watch, so I can work out without my iPhone, but having some fresh streaming was the main reason I signed up for Apple Music. It is so nice not having the iPhone bouncing in my pocket while working out, and health data tracking on the watch is an added bonus.