Dont see a need, unless you change your setup and style of putting, or throw a putter!

Agreed unless you change the way you putt there should be no need to be fit.

I have been using the same putter for 3 years now and I see no need to change what works. The shaft is becomming loose - can that be fixed ?

Yes you can replace the shaft or take the shaft out and put it back in so that the glue is fresh. Over the years it has probably just worked it's self loose.

Yup reshafting a putter couldn't be easier.  Just make sure you have a heat gun to pull the old or lose shaft out.  There's other methods out there but the heat gun is easiest IMO.