This is an introduction of a vulnerability.
Servers can avoid reboots for long periods of time, but not forever.
Once you need serious uptime, you will have more than one server providing the same services in either a failover / load balancing type arrangement, and individual servers can be rebooted without creating a service interruption.
Much too risky to allow realtime kernel patches for sake of convenience of no reboot, IMHO.
Depends on the situation. Some research applications can run for days at a time—and they need that uptime. This allows for patching during a multi-day/week job without having to restart that job.
This is probably another wonderful development by the NSA.
Multi system redundancy can make a good system but less than a perfect one. If a system has to drop a transaction, something suffers.
Claims of risk should be backed up by more than just reiterating the claim. There are plausible risks to an approach like this, such as both kernels needing to be able to support the kernel-to-kernel handoff and having a bug doing so. But they should be listed, not just handwaving engaged in.
Servers can avoid reboots for long periods of time, but not forever.
I wouldn't call it a 'vulnerability', but it does bring up something that can sometimes cause problems, and that is, the longer a system runs, the less confidence administrators tend to have of it coming back up cleanly after a reboot. I've seen servers go years between reboots even without this feature because they weren't being religiously patched. (They were fairly stable systems that weren't externally facing). The longer they'd go, the less confidence you'd have that you actually knew about any changes that had been made to the systems. Additionally, having long uptimes could occasionally mask hardware issues. I've seen AIX servers that pretty much ran continuously from the time the OS was installed until the next update, which in the case of these systems was about 4-5 years. For some, once the hard drive would spin down, they just wouldn't spin back up, so they were fine as long as they were chugging along, but the moment you tried to reboot, you were in serious trouble..
If your change control procedures are good, you can stay on top of any configuration changes that have occurred, but sometimes it's hard to remember stuff from more than a year back.