It became more common when they started getting most orders from the web page, but even before that, over the phone you could order whatever toppings you want. (They just didn't advertise all the options back then.) They also gave the option of different toppings on left and right to keep a family happy when they have different tastes. And since it's now on a web page, they don't have to spend time on the phone while you explain it to them.

But even back in the 90's, my dad ordered a pizza with half no cheese. (He still had the sauce though.)

We have that too. At some pizza places they're called "speciality pizzas." But almost every pizza restaurant also lets you make your own by choosing ingredients individually; they're priced by number of toppings, with one sauce and cheese being included in the base price.

My wife actually discovered that this is pretty much just a North American thing a while back, incidentally. She lived with some Europeans and a Japanese person for a little while during college, and they were all shocked at the North American pizza ordering process.