Your suggestion is very regional specific and perhaps limited to the USA
(probably fine for OP, who indicated they live in the USA, but)
In many countries, like whole Europe, its literally impossible to get a “burner number” because any SIM card requires by law a personal verification
'Burner' in this context means 'cheap enough to be disposable', not necessarily 'anonymous'. It's not about being untraceable, it's just about not pinging all the Normal People who may know your main phone number with whatever difficult-to-explain profile info/icon you want to use.
Interesting to know about Europe though. I wouldn't expect to need a SIM card at all to get a phone number where I live. (I think that's a mobile phone thing; I've never owned one. Here I have my public/private phone numbers through online services like Textfree and Google Voice.)
Man, I miss furry cons.