Should you add MX entries for hosts in your (public) DNS?
For a long time, whenever we added a new server to our public DNS,
we also added an MX entry for it (directing inbound email to our
general external MX gateway). This was essentially historical habit,
and I believe it came about because a very long time ago there were
far too many programs that would send out email with
To: addresses of '<user>@<host>.<our domain>'. Adding MX
entries made all of that email work.
In the past few years, I have been advocating (mostly successfully) for moving away from this model of automatically adding MX entries, because I've come to believe that in practice it leads to problems over the long term. The basic problem is this: once an email address leaks into public, you're often stuck supporting it for a significant amount of time. Once those <host>.<our-dom> DNS names start showing up in email, they start getting saved in people's address books, wind up in mailing list subscriptions, and so on and so forth. Once that happens, you've created a usage of the name that may vastly outlast the actual machine itself; this means that over time, you may well have to accumulate a whole collection of lingering MX entries for now-obsolete machines that no longer exist.
These days, it's not hard to configure both machines and mail programs to use the canonical '<user>@<our-dom>' addresses that you want and to not generate those problematic '<user>@<host>.<our-dom>' addresses. If programs (or people) do generate such addresses anyways, your next step is to fix them up in your outgoing mail gateway, forcefully rewriting them to your canonical form. Once you get all of this going you no longer need to support the <host>.<our-dom> form of addresses at all in order to make people's email work, and so in my view you're better off arranging for such addresses to never work by omitting MX entries for them (and refusing them on your external mail gateway). That way if people do mistakenly (or deliberately) generate such addresses and let them escape to the outside world, they break immediately and people can immediately fix things. You aren't stuck with addresses that will work for a while and then either impose long-term burdens on you or break someday.
The obvious exception here is cases where you actually do want a hostname to work in email and be accepted in general; perhaps you want, say, '<user>@support.<our-dom>' to work, or '<user>@www.<our-dom>', or the like. But then you can actively choose to add an MX entry (and any other special processing you may need), and you can always defer doing this until the actual need materializes instead of doing it in anticipation when you set up the machine's other DNS.
(If you want only some local usernames to be accepted for such hostnames, say only 'support@support.<our-dom>', you'll obviously need to do more work in your email system. We haven't gone to this extent so far; all local addresses are accepted for all hostname and domain name variants that we accept as 'us'.)