Adding a <meta> tag or creating a page with certain content are already used even for more impactful verification, like getting issued a certificate for that domain.
If an attacker does have broad access to edit the HTML of your website, I feel that's already the issue and Mastodon verifying that "this person controls this website" isn't even really wrong.
No sane sober person would use it to authenticate messages about changing URLs in a software supply chain.
How is this any different than your email address being compromised? How is this different than having your laptop compromised and somebody downloading your .ssh folder?
The issue here isn't "is this reliable identification" - because it IS reliable. Your concern is "how likely is this to be compromised vs other things" and that's a fair concern - but there are plenty of very secure web sites out there. This isn't saying "I am john doe and this is my identity", this is saying with some confidence "this person on mastadon is the same person as the person who wrote this web site copy" and that's a totally fine piece of identification for the right context.
This is in addition to the original site linking to the new one with a news post. Does that also mean nothing because an attacker could add a news post to the page?
So it doesn't confirm the account belongs to the author, it confirms the site has a specific link and nothing more.