We have been in Great Britain about once a year for the last several years and it is standard procedure, no one takes your card from the table and disappears. Everythiing is done at the table.
Having had a credit card number of ours used by some thief we thought it was a great idea. Fortunately we were able to correct that theft fairly easily, but we have friends who had a terrible time after someone got their number.
Crooks will find other ways to get the numbers but this seems like a great idea to me to make it harder for them.
There really was no down side to the process that we could discern.
Before criticizing a person, walk a mile in his shoes - then you are a mile away and you have his shoes!