What I don't get is they've already solved the problem of figuring out when you can register for your next battle, at least on the mobile version of the Battle Lobby. At the bottom of the lobby there's a list of your battles and the time remaining. If they could implement it on the computer battle lobby, I think it could go a long way to reducing the extra clicks (taking away the bottom two sort bar options at the top of the battle lobby, would be a great place for it).
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You can register earlier.
Basically, the battles have
at least the following states: Registering, In Progress, Calculating, Finished.
When you join a battle and it's In Progress, your Register button will either be "Closed" (Grey), "Resume" (Green), or "Finished" (Black).
The Closed button happens when you are playing a battle, and you click in a different lobby.
The Resume is when you click in your lobby and still have spins to do.
And the Finished is when you click in your lobby but you have done your spins.
So, if you click in your lobby or in this case, in the mobile version if you see finished, it doesn't mean that the lobby is closed as there are other players with spins to do.
How the registration is coded is that as soon as your lobby goes into the calculating you can already register in another lobby, you don't need for the server to give away the rewards, but you just receive the notification that the battle ended when all the calculations are done, thus why people keep clicking from battle to battle to check if they can register again.
To add an extra bit of complexity, that time remaining is until the battle ends, but sometimes, if the players do their spins quickly and there are a few minutes remaining but no one has any spin to do, the lobby will close earlier allowing the players to register before the intended closure of the battle.
So, from my point of view, they could add some extra code where they will keep track of the registered battles in the player's browser in order to avoid excessive requests to the server when the player is clicking on different battles and send a trigger to the player client when the battle moves from "In Progress" to "Calculation", then the site on the players computer could allow the registration again and just do a double check in the server side that the player can indeed register to the battle, avoiding a new request to the server plus the checks it has to do to check if the player can register every time the player is clicking in different battles.