I agree that this will lead to skin irritation BUT the most common, non medical, reason for paw licking - and indeed for any other self harm behaviour in the dog - is attention seeking. This not a dog being a brat and licking their feet because they know it will lead to skin irritation, worry for the owner and expensive trips to the vet. It is simply the dog telling you that it can gain control of you. At any moment the dog has learned, because of your reaction, that having a good lick or chew at a foot will focus your attention on the dog.
Obviously, get the vet check, but mention this theory to the vet and see what they say - vets are not behaviourists and I could only do emergency first aid, not surgery, on a dog!
Vet check is clear then you need to learn how to ignore the behaviour - don't look, don't speak - leave the room if you have to!
One family with this problem I got to all stand up, go upstairs and shut bedroom doors as soon as their dog started this. They had to stay in bedrooms until five minutes after they stopped hearing their gorgeous Lab moving around the house. The dog then escalated the behaviour to chewing it's feet, cushions, table legs etc. It took them three hours of consistent walking away without looking or speaking and the dog has never licked or chewed it's feet or anything else since.
The hard thing is that if something you do works - the dog will try harder with the behaviour before it gives in or it will distance itself from you (a good thing!!!) to have a think about what just happened - when it comes back to you it will be wary, not scared, ignore it and it will work it out in a way that the dog can accept and understand.