Anyone who thinks that their privacy is secured by using one form of authentication over the other has not seen how marketing platforms work. Each interaction you do online is tagged to an entity and each entity is ultimately tagged to an identity based on the relationships between entities.
You can of course not make it easy for them by sharing all your data like location and voice recordings. But that's it. Nobody is tracking you as an individual but if someone wants to, they can. There are policies that have to be followed for not storing PII (personally identifiable information) data but we don't know how much of it is being followed behind the scenes.
For example, Netflix doesn't use social login but google still knows what you are watching on Netflix. You start seeing articles about that show and characters on Google news feed. Your google search auto complete starts giving you suggestions about a product you searched on Amazon mobile app.
Based on everything you do, they know your interests, based on your interests they know your age group, sexual inclinations, your family and friends, your psychological profile etc. So far it's mostly being used to tailor products and services that you are most likely to pay for and use.
What
@mk76 said is absolutely true. Not sharing your mobile number does not in anyway mean that your privacy is secured. You can judge that from the number of spam SMS you receive despite there being strict regulations by TRAI on spam.
If you think you will get away by not sharing your mobile number, you must see some episodes on Crime Patrol and the likes. The telecom companies are required to store all your records for at least 11 years. Which includes all details like your location, who you called, for how long, from which device etc. They even know and record which websites you visit on their network. With deep packet inspection, they can track which mobile apps you are using. The top website that people open on their phones (till it was banned) is xvideos. If the telecom companies want to know (its not legal until the government wants to know) who is watching say child pornography, they can identify the phone number.
Coming to the point by
@puns, it will greatly alleviate the problem of spam by discouraging rampant account creation. It's like putting up a lock. The ones who want to steal will still break it. But people like you or me who might be tempted to peek through an otherwise open door will desist from breaking the lock.