So there are two basic espresso drinks everyone orders. A latte and a cappuccino.

A latte is (approximately) 20% espresso, 70% steamed milk and 10% foam on top. Making a latte without foam is no problem.

A cappuccino is (again, approx) 20% espresso, 70% foam, and 10% steamed milk.

So if they wanted no foam in their cappuccino, they want a latte. Probably what happens is they’re used to getting “cappuccinos” at gas stations, which are actually “lattes” (still questionable if they are lattes), and get frustrated when they get a drink with all foam.

It can, it's mostly just that we are passionate about our coffee and in tradition a cappuccino is more foam... But as has been highlighted by the 2 other responses, there isn't a clear amount it should be foam. At my store we happily ring you in for no foam and then just shrug our shoulders, we know what you want. In theory this would leave the cup a third empty though, if you just removed the foam from a cappuccino

The mixture of foam and milk is what makes a cappuccino a cappuccino. If you leave of the foam, it's not a cappuccino anymore but a (wet) latte.

A cappuccino is, essentially, 80% foam, 15% steamed milk and 5% espresso. A latte is 90% steamed milk, 5% foam, 5% espresso. A cappuccino is meant to be frothy and light. It should feel like air when you pick up the cup.

If you don't want the frothy, airy drink that is a cappuccino, just order a latte. That's why it makes no sense to order a "cappuccino with no foam." You're essentially ordering a latte.

Bonus fact, a cappuccino with flavour at Starbucks will come with one less pump of syrup!