I don't _think_ Twitter or Facebook are doing backroom deals with every prepaid sim vendor to be able to tie that phone number back the the identity used to register the sim card.
I wouldn't suggest you use this to register your Dream Market vendor account, but I doubt you'll end up with targeted advertising based on your other real-world web/app behaviour based just on the ID provided for a single-use burner SIM...
You don't need to show any ID in Europe to buy non-contract phone number. You can go into most stores and get free or pay 1-5 euro for a phone number.
Even before that prepaid phones have been a strawman argument, actually maintaining a 2nd number in the long run is quite a bit of work since it usually expires if you don't use it enough.