Worse than that, you still need a Windows server running Update Manager components and the Windows client to install updates.
I think the switch from a heavyweight thick management ESX to ESXi was a good idea, but the problem is that it leaves all management capability needing a VM or external server with all the associated availability problems a single point of failure.
Frankly, I'd like to see ESXi re-thickened a bit to include vCenter management into the base install with master/slave clustering and a distributed database. This would improve vCenter availability and reduce the dependence on a separate VM.
Every new host would then be a potential vCenter cluster management participant. Upgrading a node across version boundary would upgrade vCenter, so as the cluster was upgraded the vCenter upgrade came with the package.
The downside would be that it would require more storage for the base image, breaking more than a few tiny SD/USB installs. The write rate of vCenter may be a bit much for the media used in these flash installs, but not by much and if server motherboards start shipping with M.2 slots the capacity and write durability shouldn't be issues.