You both are correct and boy have we been through all that, from 4 kids to parties, EZ to pickup ice to not so much, etc.
The countertop is a must, whatever you do b/c of price and could be in pantry but best near a water source since YOU must fill it all the time. This ice is best on teeth if a chewer, since it is soft and only ~32F or so. It makes ice faster than the refrigerator but melts faster since ref ice is "less than 32F" others have measured - not I. When all ice makers fail you needing repairs, this one saves the day, else a new one replaces the broken one faster than repairs on the others. You must CLEAN it to stay healthy.
Always get a refrigerator ice maker, even though replacement range is 2-5 years, some have been DIY.
Scotsman Ice Dispensers are the gold standard in all things ice.
There is some health cleaning required BUT the old ice at bottom that may be suspect is melted down the drain.
The top ice maker cells fill themselves & since the water sprays into upside down cells, only the purset water sticks & becomes ice while the suspect water goes down the drain. Not any more wasteful - to be healthy - than an R.O. water filter system ... that might be hooked up to serve. Indeed 20 minutes is not the speedy 9 minute table top race car but this bin is huge serving many for hours whlle table top serves a party of two continuously.
Bottom Line:
1. Countertop a must (serves 2)
2. Rrefrigerator ice maker - no excuse (serves 3-4)
3. Scotsman IF there's no store bought ice within 2-3 minutes drive and a huge ice chest on wheels to hold it all.
BTW the more you own, the more they own you in time, repairs, first & running costs ....
but ice is worth it!
Ten words or less ... a goal unattainable