But wouldn't you cross check the altimeters after you have set 1013 on climb or QNH on descent?
Why specifically check them at 10 and 20 k?
OK the 10k call is there for other reasons - perhaps pressurisation on the way up and/or MSA going down etc.
I can assure you that the check every 10,000 ft originated because of misreading 3 pointer altimeters and it stuck after the servo altimeter (with digital readout) become commonplace.