Love mullvad, if you seek a truly privacy loving VPN provider look no further. Smart company, smart payment system.
If you don't trust the network you're on, use Mullvad. If you want to appear as though you're in a different location, use Mullvad. If you want to bypass your network's firewall, use Mullvad. If you don't want the service you're using to see your true IP, use Mullvad.
But most people don't need a VPN running all the time. Or even most of the time.
And while yes, you don't provide your personal information directly to Mullvad, it wouldn't be very hard to deduce you from your traffic with some amount of effort.
No more than any ISP, and (in the USA) they're pretty universally going to spy on you, so even if (ex.) Mullvad is a coin-toss it's a win.
That site is now storing the link between your IP address and that other information. Some of those will be hacked, leaked, aggregated and combined with other datasets at scale.
Of course, your ISP/employer does know that you're visiting the Internet cafe, and in the case of work (and some ISPs) can stop you from doing so.
If you visit a website from an Internet cafe, the website may still be able to figure out who you are, just like they can when you bounce between different networks normally. And of course, if you login to your account on a website or put your shipping address or something in when buying something, you're self identifying (unless you have throwaway accounts or forwarding addresses or whatever). And finally, if someone really wants to figure out who you are to a high degree of confidence, they will.
I find this lands pretty well and is close enough to being technically correct without getting into the details that non-technical people would start glazing over if I got into.