I'm not sure we'd use AppArmor much even if we could
The news of the time interval is a string of local privilege escalation vulnerabilities in Linux (in part in the kernel). We very much need the security boundary of Unix logins, and some of these vulnerabilities are mitigated or blocked by various Linux kernel security modules ('LSMs') (cf), so I've recently been thinking if we'd use AppArmor, the LSM that Ubuntu supports.
(AppArmor didn't block as many of the vulnerabilities as a proper SELinux setup did, but SELinux needs distribution buyin and that's not what Canonical provides.)
We've traditionally disabled AppArmor because it's had issues in our environment of NFS home directories in our own locations for them (also). So let's assume that AppArmor magically works now for NFS home directories and other directories (or can easily be set with tuning knobs), and still provides meaningful security afterward. Setting up AppArmor for our environment will take some amount of work (cf), so the question is how much protection against local privilege escalation we get.
Roughly speaking, our systems fall into two categories; systems that normal people can access and run programs on, and systems that are purely for services (including things such as IMAP mail). For services, in theory we (or the people writing AppArmor profiles) can work out what the services should be allowed to do and not do, and thus lock things down against local privilege escalations in kernel systems that the services shouldn't be touching anyway (and other vulnerabilities, such as information disclosure from reading files the service shouldn't be accessing). However, this protects against an unlikely set of chained issues, where there's both a vulnerability in a service itself and then an additional vulnerability in the kernel.
(If these issues aren't unlikely, we have bigger problems.)
That leaves the systems where normal people can run their own programs (which are the ones where we really need the security boundary of logins). On these systems we have to assume that an attacker can gain the ability to run relatively arbitrary programs, either by compromising an account outright or through, for example, a compromised package that people are using in the code they're writing for their research (or a compromised editor extension, or etc; there are lots of ways in). Since people are effectively running arbitrary code, we can't protect ourselves by having AppArmor restrict what specific programs can do the way we can on service-based machines. Instead, we have to find and inventory kernel features that people will never legitimately use, and then block them through AppArmor rules.
(This is how a strict SELinux setup appears to protect against the recent vulnerabilities; a normal login is simply not allowed to use, eg, RDS sockets.)
The Linux kernel has a lot of features and facilities, although some of them are blocked off because we don't allow user namespaces, and people doing CS research do a lot of things, some of them at least unusual. Could an AppArmor profile (or a set of them) be written so that people would be allowed access to what they use and not allowed access to things that they don't? Probably (although AppArmor is more focused on programs than on people, well, logins). Would we be able to find an out of the box set of AppArmor rules and so on that worked? Maybe, and this depends on exploits not being found in areas that people pretty much have to be given access to.
If we had a reliable set of AppArmor or SELinux profiles, we might well use them because it would be easy enough. Without a reliable set of AppArmor profiles, I'm not sure we'd try to build some ourselves unless we were desperate. And if we were going to do the work, it appears that we might get more results for less effort through things like explicitly blocking all the loadable kernel modules for Linux socket types that we don't use.
(Some people even block all kernel modules that their current configuration doesn't use. I'm not sure I'd go that far, but I suppose you can always un-block things like the netfilter modules if you turn out to want to add some nftables rules later.)