I'm not sure how much is the activity of toribash players at this time but since I stopped playing, now I always see players in either bet servers or Etournies, rarely on any public servers.
There shouldn't be a rule such as not hosting Etourney while betting because most people prefer Etournies because its fun and everyone gets a chance to play rather than in bets servers where its all rigging and pay-to-play.
But as I mentioned earlier, toribash's activity is going down. So we need both tournies as well as bet servers. For the solution, the ES as well as Bet hosters should be mindful to only host 1 tourney or bet server each day so both have the chance to host equally.
Because Etournies mostly remain for 1 hour while bet servers go up for more than 2 hours at times when a lot of activity. So even if there's a tourney going on, bet server can be revived after an hour or so.

Just a suggestion/advice for ES to not pick extra-long mods in tournies. Consumes a lot of time for each and everyone to play.