I have never had a run in with a mugger, and I doubt that you have either. The scenario that you are describing is highly unlikely.
On the other hand, I HAVE lost my phone. Requiring fingerprint authentication would prevent somebody from being able to use your phone to buy things. I would much rather take the risk of losing my finger in the mugging scenario you posit (statistically will never happen to me) then take the risk that losing my phone = losing everything I have in the bank.
To put your scenario in perspective, if there is no fingerprint scanner included on your phone, then payment security will be in the form of a number/question that you need to answer in order to make a payment. Conceivably a 'crack-head' mugger could capture you and torture you until you give up your information. Like finger-chopping, this is highly unlikely.
I really want my phone to replace my wallet. The way I envision the future of mobile payments is this:
-Credit card readers will all have NFD sensors installed on them.
-Payment will be made by activating a payment app and then passing your phone over the NFD sensor. A digital signature will then be requested by your phone. This signature can take the form of a security question, fingerprint, PIN code, etc.
-A digital receipt is transferred to your phone
A system similar to the one that I describe above would make tracking expenses very easy. You would have digital access to not only how much you spend at a given store, but exactly what you purchased. Budgeting would be extremely simple because the daily input of data that a good budget requires would be almost completely automated. You would suddenly be able to see exactly what your shoe addiction costs.
Yes, there are security concerns to consider with a mobile payment system. The company (hopefully mine ) that ultimately creates the mobile payment system that we all use, will need to consider everything from your far-fetched mugging scene, to the more realistic possibility that your entire purchasing history/location/habits could be packaged and sold.
Fear is no bedfellow of innovation.
No this is why finger print ID has never been used on cash machines, if someone is willing to beat the crap out of you to get you to tell them your pin they are perfectly capable or razoring off a finger. And yes I have been mugged and it isn't a pleasant experience getting a knife held to your back to get you to divulge your pin after they have already punched you in the face a couple of times to soften you up a bit.