In short: You cannot simply set up a rogue Google or Reddit e-mail server, because DNS.
E-mail clients and servers rely upon DNS in very much the same way most web browsers and websites do. When a node has a package that requires delivery to an address at
domain.tld, that node will first query their DNS servers to retrieve the MX record for that domain. The MX record, in turn, points to the registered IPs or hostnamefor the e-mail servers for that domain.
Even if you set up your e-mail server, and configured it to accept mail for
domain.tld, it would never receive mail for that domain unless the person in control of the domain's DNS included your server in their MX records. Of course, there are ways that DNS could be spoofed or a system could be pointed to a rogue DNS server. But those are beyond the scope of this discussion.
Aside from making sure you're not trying to set up a spoof mail server, the dependency upon DNS is another reason Google and similar services require this type of verification for custom domains. The verification process requires that you post a unique string in a location which requires a DNS lookup to reach. If the service provider can verify that you have posted the string there, then they know that you at least have control of the DNS records for that domain.
(Whether control of those records was legitimately obtained is, to a certain degree, not their concern. It's largely up to the DNS provider to make sure unauthorized users cannot modify the records.)
If you don't have control of the DNS records, then no e-mail provider will be able to service your custom domain. Thus, why would they go through the trouble, and expend the resources, to set up a server that won't provide the functionality their customer expects?