I had thought about it quite a few times and seen some people utilize this method, but here are my thoughts why I didn't (mainly cause I gots 4 wheeler usage)
It really limits your ability to hunt.
If you leave it and pound the shore line hunting, you still need to walk back along the shoreline to where you left it. And it is tough riding it over the dirt roads with fish.
I have found that it is just easier to make the hike to sows (about 30 mins) or Churches or out to the cut (Impossible to ride a bike out to) and it isn't worth the hassle of dealing with a bike.
fished cutty last year for the first time. i fish montauk a lot more as i am originally from LI. i don't think you can compare two of the most beautiful places in the world to striper fish. cutty has it's own charm. as does montauk, as does block and any of a dozen other legendary haunts. fish'em all if you can. if you go to only catch fish, wherever you go, and will be dissapointed if you don't, then let me know the formula for not getting dissapointed!