Two questions which I don't think were brought up in this thread yet...
When you miss on short putts (under 5 feet) vs long putts do your miss left or right? (assuming you are right handed).
Have you setup for a putt and feel like you are aligned, then put your club down along the toes of your shoes, step back, and see which way left, right or parallel to the path to the hole you are favoring.
These are two things you can learn about your general putting strokes that if in fact you do go for a putter fitting you should be prepared to let the fitter know. They should ask you "do you generally miss left or right?" Then they should be inspecting your alignment to a straight no break shot. The second one might give you some real insight without spending a dime! I miss left and I also line up left without realizing it! If you actually arc more naturally and push left, then the recommendation will likely be some degree of toe hang to stabilize. If you do both arc AND set up left unconciously it will be even worse. Better to address alignment than to get a really toe down putter head since if you fix alignment then you may miss right. I have not been fit, but since I know my tendencies I would be looking for from the technology (and the fitter's expertise assuming they have any) is what is the right length of club and lie angle for my natural stroke and then what face balance best suits my natural swing.
Is it worth the money? Only if the fitter knows what he or she is doing, and then only maybe or if nothing else to satisfy your curiosity so you don't keep wondering if a fitting will help. If you have a lot of putter swing thoughts, then all bets are off until you feel natural. Just physics of the brain and muscles I suspect.