TheFragileI typed out a bunch of stuff, but it was really just me shitting on CEVO and saying "well, ESEA does this fine for the most part, but it could improve."
If I had to directly compare it to ESEA? Hm, I'll name a few things really quick.
Take what ESEA has, and then have better servers, either no client or a client that actually works / catches cheaters / doesn't run as a process in the background, more TF2 content on the website itself or at least direct itself to TFTV for the content, having the maps played in the season actually consistent (ie: I think my team has to play Metalworks once this season and Process four times? Why?), more diverse stats like sizzlingstats, and a few other reasons I probably can think of later but can't think of now.
I believe the scheduling issue is because ESEA schedules Invite over 9 weeks (where the week 1 map is repeated in week 9) even though there are 8 teams and 16 matches per team, so to make up for it some weeks a team only has one match to play that week. It's weird but that's how they do it.
GentlemanJonIt doesn't really sound like there's a huge amount of room to improve on ESEA, most of these things seem indicative of a lack of love over the years (like the stats slowly becoming a little antiquated), the stance on no client would be the controversial part. Would people pay to play knowing Vac or a volunter AC team were the only defence?
Also servers, are we talking about TF2 being held back on old hardware or is it locations, routing, or what? Or is it just the usual server situation - nobody is ever completely happy? The website could be modernised massively but that's really secondary to things just working.
Given how prevalent cheating is becoming in TF2 recently, I doubt people would be satisfied enough with VAC or volunteer AC, though whether they'd still pay for it would be debatable. Even with everyone paying league fees, though, you're still talking about a massive reduction in prizepots without new sponsors somehow getting involved.
For servers, I believe the issue is much less prevalent than it was a few seasons ago where there would always be stutters every 5 minutes. Honestly, I believe the main issue now is just locations, as there's no one location that satisfies everyone in North America.