You definitely underestimate the effort it takes to run this type of tournament.
I don't have experience in osu! tournaments, but I have been hosting tournaments and currently a league in RocketLeague for years and I think the effort should be equal to that.
For osu! you'd probably have to have a set mappool that changes in a certain interval, you need people to sign up every week and you need some way to get those random people to form teams, as well as someone who administrates the tournament or you will have A LOT of work to do...
My recommendations from my RocketLeague background:
1) Don't make the tournaments too often. Keep it regular, but every week is too often.
Most people only have time at the weekend or troughout the evenings. But you have to count with the time the most people can play - weekend.
So you'd have 2 days a week where people CAN play (at least one day) for sure.
So the tournament would have to be on the weekend.
So Monday - Friday = preparation, Saturday + Sunday = tournament.
Preparation is key
I would recommend you to host it every 2 weeks. That gives you, your staff and your players more time to prepare.
2) Be clear about the process the tournament runs.
Like play it through, from start to finish. Does it work out? What are the problems people could run in to and ask you.
How can you provide them with tools to make the process of signing up, as well as team building easier? (e.g. Discord, Spreadsheet)
3) You have a pool of random players with random skill. Keep that in mind.
You'll need to decide a difficulty for the mappool. Also think about how you could prevent people from forming high rank teams against low rank teams. How can that be prevented?
4) How professional do you want to tournament series to be?
You can make to professional and put in a lot of work, or make it un-professionell and make yourself an easy life.
But keep in mind: The more you pre-think, pre-plan and preparate, the better the tournament will be received and the higher the propability of people resigning up.
----------------------
So yea, the 4th point said it all.
Your idea can develop into a great and well received thing, or it can be a one-timer that is gone as fast as it appeared.
If you want to make the move and create this series: make the process as easy as possible and as error-free as possible for your players. Every great tournament series started small once.