I have the Mary Jane
Crocs and I love them! I wore them when we went to WDW last month- traded them out with Beach and Cayman models. I had no problem with the strap at all- and I have really high arches. I just stretched the strap out a bit when I got them. I didn't have any rubbibg at all.
The only thing I noticed with the Mary Janes was that they weren't quite as comfy for walking around WDW for a full day as the Beach or Cayman models. I think it has to do with the fact that the MJs are more streamlined and have a bit thinner sole than the others. They are still fine for around town, but my feet were a bit sore after a full day at WDW.
I love them, though- they are "cuter" than the origional Crocs- not as clunky looking. I wear them all the time.
* I also just got some of the NEW Croc sandals- the Cleo style. They aren't available until March 1st on the Croc website, but my local Dick's Sporting Goods store had them in stock. They are super cute, and seem really comfy so far.