I'd agree that these two are probably the most fully-formed of Jesse's contributions - up there with decent (but not brilliant) Whyte/Boorer album tracks. I liked On the Streets as well.
I think his stuff, as 2D as it is, brings out some good vocal melodies and energy in Morrissey. A lot of people don't like I'm Okay... but I think it's a strong album closer with plenty of vim & vigor as far as Morrissey himself, if not interesting musically.
I've said it often but Jesse's stuff has a forward propulsion that I like is but Very thin on ideas. I think if you took a typical Jesse track and then had another songwriter + alpha to it you could have something special.
As is, Jesse will probably not (after 7 years) get beyond where he is now and may very well get lazier.
I tire of the constant calls for Morrissey to sack his band. I'd like to see some new collaborators but if that's who he works well with then so be it.
However, he could threaten them with demotion or firing if they don't come up with something better! Might scare up some sparks of brilliance.
I remember a story about Brett Anderson locking Richard Oakes in a hotel room saying he had to come up with songs or be ousted. He's not as good a songwriter as Butler but he did come up with some great stuff for Coming Up!
"In The Future When All's Well" and "You have Killed Me"