There are a lot of answers here but I feel they mostly miss OP’s point so I’ll try my own:

What stops a scammer from HTTPS certifying foobar.reputable.com is the trust system.

Anybody can create a certificate on their machine for anything within seconds, even you could create a certificate for www.google.com. The problem is that you, as an issuer, are not trusted by anybody.

Browsers and operating systems are released with a list of issuers that are considered trustworthy, so if you want your certificate to be recognised it has to come from one of these, not from you.

All of these issuers are in the list because they have been individually vetted, and are known to do their due diligence before issuing certificates, so they would not give you that cert unless they know that the bank domain or subdomain belongs to you, and the technical means to achieve this have been explained in other answers.

But if one of these issuers went rogue, or if you hypothetically hacked into their certification authority, then indeed nothing would stop you from obtaining a valid and recognised certificate for foobar.bank.com.

This is why for example Trustcor was removed from this list in 2022: from that position it would be trivial for a certificate authority to allow third parties to spy on people.

I recall that subdomains are their own record inside a DNS

Well, not a record, but a zone. A subdomain is its own zone. There are additional DNS records that support a separate zone though.

which would imply that anyone can claim that their server is a non-existent subdomain of the real domain

False. The person wanting control of the subdomain must be delegated control from the parent domain. Owners of the parent domain don’t just hand that out to anyone. The mechanism is called DNS Delegation.

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