In the US one can buy a prepaid card wearing a mask and paying with cash.
Also I came across this service which purports to be anonymous: https://www.cape.co/ but has a ridiculous monthly fee.
Half of the eastern EU countries have no ID requirements.
Not to say they're not moving towards it, but it's not that dire yet.
Case in point: recently, some Russian mobile service providers started blocking registration SMS for popular messengers, Signal included.
In earlier years there were also cases of mobile number spoofing in the country, where the control over the number was given to law enforcement who then use it as second factor authentication to break into different accounts.
That's how easy it is. The word "secure" and "mobile phone number" are the opposites of each other.