Nobody should be penalized or have fingers pointed for playing under the site and table rules. Rules which include expelling a player for being more than 20 seconds out of time in real-time tables or whatever it is in turn-based.
There are several reasons for doing so but none are actually needed. The player hitting the red button needs to provide no justification.
This works fine for 2 player games but not so much for multiplayer games because the expelled player is not always the only one punished for this. What to do?
Create a table and click the [Modify] button. Next to that button it usually says (no presentation yet). Type : "Expelling only by majority vote of those present." Or some other house rule you prefer. It needs to be very short since the site does not allow a long message. But you can just type a longer explanation and copy&paste it each time someone joins the table, make sure to do so before the game starts. No new house rules should be allowed after the game starts, of course. Probably might need to add that expelling is fine after some time, say 15 minutes for real-time or whatever for turn-based, even without majority.
The site won't automatically enforce such house rule. But most people would respect it if they join. Surely more than your current case of no house rules. And if someone infringes you can report them and I assume action will be taken by the site administrator, which would not happen without house rules.
If such house rule becomes popular among your peers you will see other people starting tables like that.
If it becomes REALLY popular BGA might even implement it. Surely being proactive yourself and getting a following is the best way to show BGA that this is a needed feature.