Cryptographically it seems as though all we need in HTTP is that we get back a special token when we ask for it. But it's essential in designing real-world security systems to understand real world practice. Historically (prior to the Ten Blessed Methods explicitly forbidding this) it was not uncommon for HTTP-based DV to go like this:
Customer: I want a cert for www.example.com
Average CA: OK, put this file (containing the text 12345678) on http://www.example.com/average-12345678
Customer: OK done.
Average CA does GET http://www.example.com/average-12345678 verifies that the token 12345678 is present and issues certificate
Cryptographically it's fine, who else but the owner could make this test pass? But in the real world lots of web servers when you ask them for average-12345678 will go "Sorry, average-12345678 isn't available. Maybe you'd like to visit our home page?" and that text matches the token and passes the test.
That really happened, to real commercial CAs which are still trusted today, because they hadn't thought about real world problems (also in one case because they goofed an HTTP response code check so if you gave that reply as a 404 their code wouldn't notice it was a 404 before passing the test)
Let's Encrypt was designed to prevent this mistake (even though embarrassingly it was still happening at other CAs years later until the Ten Blessed Methods were de facto imposed by Mozilla policy) but managed to make a very similar mistake in tls-sni-01 which was dangerous because Apache httpd (and maybe nginx?) has crazy default behaviour for virtual hosts on HTTPS. Again, in principle tls-sni-01 looks safe, who else but the real owner could answer TLS setups with bogus SNI information? But the real world gives us an answer: Anybody sharing a cheap bulk hosting site with you if the host used one of the world's most popular web servers.
You can see analogues in the real world too. We had a sub-thread on HN recently about RFID entry badges. Most use a very passive design which is easily cloned. But you can buy hard-to-clone secure systems for this role. Having done so you might assume only employees and legitimate visitors can get into your facility. And then you see that in the real world your employees are still letting people tailgate and leaving fire doors open to take a smoke break and you realise that cryptographic security of the RFID entry cards was not in fact your big problem in controlling which people are in the building.