Sounds like a great idea for starting a riot. Or a revolution.

An interesting idea.

But:1. stores can abuse it - say you put 1 cheep line an 19 expensive, this will cause all average customers to pay extra fee (assuming this store have some kind of monopoly over the customers e.g. store in remote area)

2. If you have one expensive line an 19 cheep lines - the expensive line needs to be significantly expensive otherwise it will be flooded and will not be short anymore.

3. The most important thing to investigate is the customers reaction towards such mechanism ..., people might resent the need to select...

There are many way in which this idea can be tweaked in order to balance different factors ...

People of wealth have their help doing the shopping. But let's say we are talking about people who just have little patience.
The credit card reader at each cashier register would have an additional option for "Personal Service".

After pressing the button, a display would come up and ask the customer scan their credit card, "Do you agree to pay $5 in addition to your purchase for having personal service?", the customer selects "Yes", a buzzer sounds and the managers pager calls them to take care of the customer immediately.

The system would have a lockout so managers could lockout this option when there are not enough clerks to spare.

Sorry, left out one vital piece of info. The customer wanting "Personal Service" would go to a cash register where there is NOT a clerk present. Then press the "Personal Service" button on the card reader, then scan their credit card.

The money should go to the people being cut, not the store!

How about just having a register with a posted-five-percent mark-up--most people won't choose it, so it would by design have a short line at all times.

Yes, the money doesn't go to the people waiting, but I really don't think it should.