Inherently, not really. An expired, self-signed or even incorrect (as in, the wrong domain is listed) certificate can be used to secure a connection just as well as a perfectly valid certificate.

Rather, the purpose of all of these systems (in theory) is to verify that the certificate belongs to the correct entity, and not some third party that happens to impersonate the original. It's not just security, but also verification: how do I know that the server that responds to example.com controls the domain name example.com (and that someone else isn't just responding to it because they hijacked my DNS.)

The expiration date mainly exists to protect against 2 kinds of attacks: the first is that, if it didn't exist, if you somehow obtained a valid certificate for example.com, it'd just be valid forever. All I'd need to do is get a certificate for example.com at some point, sell the domain to another party and then I'd be able to impersonate the party that owns example.com forever. An expiration date limits the scope of that attack to however long the issued certificate was valid for (since I wouldn't be able to re-verify the certificate.)

The second is to reduce the value of a leaked certificate. If you assume that any certificate issued will leak at some point, regardless of how it's secured (because you don't know how it's stored), then the best thing you can do is make it so that the certificate has a limited lifespan. It's not a problem if a certificate from say, a month ago, leaks if the lifespan of the certificate was only 3 days.

Those are the on paper reasons to distrust expired certificates, but in practice the discussion is a bit more nuanced in ways you can't cleanly express in technical terms. In the case of a .mil domain (where the ways it can resolve are inherently limited because the entire TLD is owned by a single entity - the US military), it's mostly just really lazy and unprofessional. The US military has a budget of "yes"; they should be able to keep enough tech support around to renew their certificates both on time and to ensure that all their devices can handle cert rotations.

Similarly, within a network you fully control, the issues with a broken certificate setup mostly just come down to really annoying warnings rather than any actual insecurity; it's hard to argue that the device is being impersonated when it's literally sitting right across from you and you see the lights on it blink when you connect to it.

Most of the issues with bad certificate handling come into play only when you're dealing with an insecure network, where there's a ton of different parties that could plausibly resolve your request... like most of the internet. (The exception being specialty domains like .gov/.mil and other such TLDs that are owned by singular entities and as a result have secondary, non-certificate ways in which you can check if the right entity owns them, such as checking which entity the responding IP belongs to, since the US government literally owns IP ranges.)