I'm just speaking for myself, but I putt from the fringe all the time, with fairly successful results. Now, if my lie indicator says I have, for example, a %10-15 lie, I will not putt, but rather chip, pitch, or flop.
Also, don't forget to watch your meter strength when on the fringe - with the beginner putter it will default to 150 feet. I've hit many a chip shot back on the green after putting it onto the fairway by not paying attention to my meter.
And, as was said earlier, I've even putted from the fairway myself at St. Andrew's, because any other shot would not put me close enough to the pin. It's all about picking the right tool for the job.
And, like with everything, it takes a lot of practice and experimenting
to find out what works.
Good luck, and don't give up.