I'm going to assume you are fully aware of all the risks of induction - that you may be inducing an early baby (due dates aren't always right, and a pregnancy may not be complete until 42 weeks - depends on your baby!), that you are increasing the risk of foetal distress and caesarean section, that you will probably have to have continuous external foetal monitoring, and there are risks involved with an amniotomy. There is also no guarantee that an induction will be successful. There is also no guarantee that you won't go into labour before your induction is scheduled, and you'll have to make contingency plans for all those concerns of yours anyway!!

Anyway, assuming you are at peace with all of that, yes, some OBs will do inductions for "social reasons". My last was much like that - I had horrible symphisis pubis pain and was miserable. Some may check how favourable your cervix is before consenting and won't induce on an unfavourable cervix. I also had an induction with #3 because like you my labours were fast, and I had to travel for over an hour and a half through mountains to the hospital. I was ready to go at 39 weeks + 3, and it was an easy induction.

Only you can know whether your request is reasonable or not!