Nice to see someone else complaining. Rather than insult you as a lot of members do to make themselves feel better. Let’s list some reasons why the arena is important to players other than those looking for a trophy count. And also ways Ludia can solve these issues outside of the Tournament.
Here are a few I can think of.
Alliance membership (having a trophy score is one way to tell it a player is active. 0 trophies can get you booted in some places)
a third tab at the top of the screen (Campaign - Tournament - PvP)
Max Tournament level reached still governs the Incubator unlocks but Incubators can be earned in normal PvP. In this PvP mode opponents would be select based on team only and not trophy count and the arena background would be random each match. Here you can select boosted or unboosted and Rarity level. so, you can go all rarity levels or just common, rare, epic or whatever you want (rats only legendary lol). Just like the Tournament AI will be used if no opponents are found. These battles count toward missions too
As for the Activity thing maybe a green light for active past 24 hrs, yellow for past 48 hrs and red after that.
@Ned Please pass this along. It will help solve a lot of conflict and allow players more freedom to battle as they like best. Even some players that never go near the Tournament might enjoy this option.