You don't do it each time, you keep a single prepaid SIM as your "spam number", like people have spam gmail accounts for online competitions and random crap.
I've been doing this for years. I have a $2 prepaid sim in an old phone sitting in my desk drawer. It's always off, and I only turn it on to approve a new signup or something. That way they can sell my number to marketers as much as they want, it doesn't bother my "real" number with robocalls and spam texts.
What's mostly surprising is the insane increase in spam texts in the last year or so of using this method. I used to turn it on once a month or so to sign up to a new site, and have a few random texts... these days I get dozens a month, only proving more than ever that this method is worth doing.
That still allows geolocation. But one can lease hosted SIMs. Actual SIMs in server farms. So they're "real" mobile numbers. Just not located where you are.
I doubt twitter is going to get your cell tower location just from your phone number. Sure, the cell provider has it and is probably keeping it around, but unless you attract significant attention to yourself (eg. bomb threat), it's not going to be disclosed. If you're really paranoid you can use it a few blocks away from your usual location.
The ToS of those providers prohibit the use of that except with explicit consent. I'm aware that the providers do little verification that consent was given, but I'm doubt that established companies such as facebook or twitter are going to risk a PR fiasco to get better anti-fraud numbers.
