Outdated and nonsensical sign-up method for the only tournament that matters, classic.
Having rankings tied to a system in which you need luck to even participate is just plain silly.
I'm sure there's a plethora of better methods, off the top of my head:
Allow it to be 32 teams and split the tournament in 2 evenings, random seeding would mean that you'd tweak your ranking system numbers accordingly.
Hold a separate TT for beginner teams, league A & B based on past performance, shuffling every X months with teams going up and down. You made a ranking system, flawed but it exists, make use of it?
Give TC an active role in TTs, holding trials for fresh teams to accept/deny entry in the competition. We've seen fresh teams take a spot over established teams almost every month over the years. I personally don't mind it but I know some do, that could be an option to explore.
Tie TTs to automated tournaments, teams holding players with the highest win% / finals appearances / whatever you deem a sufficient treshold of competitive presence would be granted a spot, that's how you'd decide the bracket, not only promoting TTs as the endgame content that it has always been but also increasing your automated tournament turnout.
People who are more invested likely have even better ideas, my point is this:
TTs feel and have historically felt less professionally held than community events like PSL, that should never be the case. Whether you like it or not, having only 1 staff member communicating here is sad.
Players jumping from team to team right before TT to guarantee a spot for themselves tarnish the integrity of TTs. It should be a team effort, not a piggybacking effort off of one talented player. Too many times we've seen easily recognizable names in fresh / different teams for them to jump back where they came from when TT ended. Crack down on it, I assure you it is always done pretty blatantly.
This is for the devs: teams are an integral part of your game design, the endgame content for competitive teams is TT. I'm in disbelief at the fact that this little attention is given to it outside of its own bubble of competitive players. With the player growth you have seen it should be a surprise that only 30 or so teams even sign up as only 3 people are technically needed. How many staff members do you assign to designing and running it? How about more? As a first step how about 1 staff member that can manage the languages you support? You'd likely avoid this: