Well it seemed important to me, change that data if you had an account with them. I try to give out as few details as possible on the internet, for example I think it was Steam that asked for a phone number on a transaction or maybe buying games elsewhere. You never need to put in your phone number. in fact I question adding a mobile to an email is a security improvement, you could just use another email. Save passwords on paper not digitally, that also gives you a list of all the online companies you have accounts with.
https://www.bbc.co.uk/news/technology-54958782
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Authenticator has to be removed before it can no longer be used. Plus only you know the back up codes. Email can be changed by anyone who has access to your account. I am probably explaining this badly but the authenticator connected to your phone is a safer way to protect your Steam account in my opinion.
Still, I recall the time when I wanted to buy a particular game and I couldn't find it anywhere. I then, as a lark, looked for it on Steam (I hadn't used Steam at this point) and lo and behold it was there.
Minutes later it was downloading.
I guess it's a tradeoff. People just have to be smart and change their passwords often. Maybe even use a "gaming e-mail" over your personal one.
Godfred's Tomb Trailer: https://youtu.be/-nsXGddj_4w
Original Skyrim: https://www.nexusmods.com/skyrim/mods/109547
Serph toze kindly has started a walk-through. https://youtu.be/UIelCK-lldo
I will look into mobile verification, I may be being too much like a dinosaur there.