Hello,
I'm not sure what would be the best thing to do, and I'm not sure that your propositions would help well for situations like tournaments.
The advantage of the current behavior is that it's crystal clear: you have no risk to accidentally forget someone or include someone in error.
As a game master, the simplest and safest to do is to open the table, make it hidden, invite the players you want to play with, start the game, and only then make the table visible again. In this way, those who join the table will necessarily be spectators.
The difficulty with a list of players to include in the game is that it has to be updated live. It's going to produce a lot of bugs of the kind including someone, and then by the time you confirm the list, that player left.
What to do with that ? Take another player at his/her place at random, or take the next one in join order ? Just starting the game without that player isn't possible as easily in all games, think about games like jass, spades or belote where the game is maybe completely impossible, or at least totally different when you are playing with two teams of two or everyone for him/herself.
There are already bugs related to that kind of behavior and it happens all the time, this is the nature of all online games, so I don't think it's judicious to complexify the thing. And at the end, it won't prevent you from selecting the wrong people.
Without a list of players to include in the game, it's going to stay unclear. If we take the 10 first to join the table, there is still great chances to include someone you didn't want, or to forget somone you wanted, simply because he/she joined too early or too late.
Really, again, the best thing to do as a table master is to make the table visible only after the game has started.
However, maybe we can talk about turning on spectator mode automatically in some situations.
For example, if you join a table with a game already in progress, it could be the case, so to avoid being accidentally included if the game has to be restarted. But it isn't so simple, since you can then have your spectator mode turned on without notice.