On a kitchen worktop with constant hot and cold then cleaning, a wax stick will not last. also look up the price per metre of cheap worktop, then compare to the price of buying a whole pack of milliput that you will keep most of in a drawer for the next 10
years.
You could use a circular saw to remove a 1 meter slice of worktop for almost the same price as your pack of milliput in white, I have some and after 20 years I still have most of the sticks, but it does not seem to fully set any more...
Wax sticks work for a french polish finish as that is always cleaned with care and not so frequently. you can peel fragments off a wax stick with your finger nail, no knife required, how well will that stay on a busy kitchen surface.