Why do almost all the cell phone numbers have no 0’s or 1’s?

Many years ago—over two decades ago, actually!—I got a cell phone for a family member. I thought it would be fun to have a phone number whose digits spelled out a word (when converting to the 2 = ABC, 3 = DEF, etc., code of the telephone). I had the impression that you could pay the phone company some extra fee and you could pick the number, kind of like a vanity license plate or those businesses that have numbers like CAR-WASH or whatever. It turned out that you can’t do that for a cell phone, or at least this provider didn’t do it. So I said, ok, just give me a number with no 1’s or 0’s, and then I can make a word out of it myself. The person on the line said they couldn’t do that either, but they could give me three numbers and I could pick one. So they gave me three numbers, but all of them had at least one 1 or 0. The person said, no problem, I’ll give you three more numbers. Again, all had at least one 1 or 0. We went through this about five more times and then eventually a number came up with no 1’s or 0’s. So I took it. It didn’t make a great word, but I was able to come up with a reasonable two-word phrase.

I know a lot of people with cell phones, and just about everybody has a number with at least one 1 or 0. I don’t know what’s up with that. There are 7 digits, the first of which can’t be 1 or 0. If the numbers were assigned purely at random, the probability of the number having no 1’s or 0’s would be 0.8^6, which is 26%.

So something’s going on here. Where are all the numbers with no 1’s and 0’s going?

The above question came up in a comment thread. I’m well aware that, back in the old days, there were rules for area codes and phone numbers (all the area codes had 0 or 1 in the middle and none of the three-digit exchanges did), also various reserved numbers such as 411, 911, and 555. But I don’t see any connection between those rules and the current practice where almost all the cell phone numbers have no 0’s or 1’s.

Whassup?