Ya know, I miss the old ways of the Saints Row series. I'm sure people have already said something like this, I wouldnt know because I havent been on here in a while. But anyway on to my point. I think the Saints Row series can be best described as a group of kids, Saints Row one and two are the two kids that everyone likes (the gamers) but the parents dont really approve of (the big game review companies). But Saints Row the Third is the kid that all the parents like and encourage their kids to play with them. The kids play with it but they're forced to take it out and buy toys for it (DLCs). Saints Row the Third used to be social friends with SR 1 and 2, but then traded its friendship for the parents approval. You can still see the influence of SR 1 and 2 but Saints Row the Third mainly tries to please the parents.
So anyway, I like Saints Row the Third, I just fear for the direction of this game. Well that was my little speech/metphore.
I agree with some of the old elements that I enjoyed are missing and wish they were included in this game, but those elements went missing in the second game as well.
I felt SR1's multiplayer was far more competitive and had contained more depth by having the ability to create "gangs"(clans to nerds). The game modes in SR2 felt awkward to me, and lost the touch of the original(which is probably why competitive multiplayer was left out this time around).
I haven't tried coop yet for SRTT, but I had a blast with it in SR2. So I can't really make any kind of judgement on it. But based on what you're saying, the series was going downhill from the second game...even tho I don't think that.