The reason Rippetoe "hates" rows so much is that everyone thinks rows are a replacement for cleans when they're really not. People repost his routine with rows substituted for cleans all the time. The reason he uses power cleans instead of rows is because cleans will cause your deadlift to increase faster since you'll be training power/speed off the floor instead of just absolute strength.
I personally don't do power cleans even though I tried to because i've had an issue with my right biceps near my elbow for years. Cleans really makes it ache. Maybe it's a form issue of bending my elbow too soon, but the issue was around before i even tried them, but very few things aggravates it and cleans and throwing a baseball too many times are two of them.
If you can, learn to do power cleans and add some chins.
Actually, i do power clean my sets of the press often.
I don't really see a big deal in rotating out any of the different type of rows movements. Do whatever row you want until it stalls and then change to another one. I did bb rows, then chest supported rows for 2 months, and am now doing db rows. But really, if you're gonna row stick with bb rows. It shouldn't really get stuck early in your career. I 'pendlay' row over 200 for 5x5 and i never did other rows until recently.
Go out of your way to get chins up too. They'll probably help more than rows will. I wish i'd paid more attention to them a few years ago.