I hope for a track based Burnout again as IMO track racing is what Burnout is. Open World might make a good game, but for me it's just not Burnout. You don't get the same close racing intensity as there is no rubber banding amongst other issues.
I am a big fan of Traffic checking, so I would like to see it back in it's full Burnout Revenge glory. I know there are quite a lot of Burnout fans who just want a Revenge 2 without much being changed except for all new and more tracks.. I am one of them!! Although having a Takedown 2 would be totally awesome too... or at least having Road Rage from Takedown in a Revenge style game!
I totally disagree with your forced matchmaking tho, as being able to control the lobby as a host is something that made Burnout a great social experience. (I recently blogged about this in "Lobbies, Hosts and Party Chat")
There is a restart option in Paradise now, it was in one of the last updates, so that was fixed. Personally I didn't need a restart as if I failed an event I just did another one instead and rarely drove back to the redo a race. At least not until my last license anyway.
Eliminator mode is cool offline, but I'm not sure how good it is as an online mode. It's not much fun if you get eliminated first and then just have to wait for everybody else to finish the event. The developers would need to make it fun for the eliminated players to make it worth doing.
Showtime isn't as good as crash mode, but it does have it's fans. I don't see why they can't have both modes?? Bringing Crash mode back is vital to make it a fully fledged Burnout game.
I really hope there will be another Burnout one day, as long as it is Burnout and not Paradise or some other game that just has Burnout in the title! 
People. Quite simply I'd like the option to mow down people if I choose to - also if I crash a bike why on earth do I not get to see the accident? I'm sure it's a rating thing and understandable as such - just annoying. Carmageddon style if possible ;) I love the open world style but that may just be due to the fact that Paradise is the first Burnout game I've owned.
- Eliminator mode in Versus and Online. I don't know why they haven't put it in their games yet, since Eliminator would be a great add-on for multiplayer.
- Forced matchmaking in Online. It's not fun when people can pick and choose who they want to race against.
- Optional traffic checking. Sometimes people just want the feel of Takedown with the graphics of Paradise. I'm pretty sure everyone will agree with me on this. Traffic checking is fun, yes, but damn it gets old.
- Restart in open world. Open world is a touchy subject, since half the burners love it and half hate it, but I think a restart function in a race will do good for a lot of people. Open world is awesome, but screw that if I have to keep having to drive back to the starting point.
- Have 'walls' when racing. It's not fun having to rely on the map to avoid getting lost during a race.
- With walls during a race, they should bring back lap races. Lap races are very intense, imo, especially when in the last laps and you're nose to nose with a Rival.
- No Showtime mode and bring back Crash mode. No explanation necessary.
- I once read an article during the development of Paradise where Criterion was going to implement a sort of crash where, if your car gets T-boned by a semi, it would literally be severed in half. Awesome.
If Criterion doesn't do this, then do you think, in the future, someone can buy th license for Burnout games and do them? Because that may be one of the goals in my life. :D