I have a consistent 25-35% cpu usage on my host with no VM's powered on. Single host ESXi 6.5. I updated to update 1 still had issue, then update 2 and still happening. If I reboot host it will run perfect for a few hours. VM's run fine and CPU usage is all good inside them. Regardless if I power my two VM's on or even leave them off... cpu will spike to around 30% in 2 to 4 hours and stay that way. It is using 6 to 8 Ghz consistently with no VM's on until I reboot...
In the monitor I see Package 0 and Package 1 are averaging 50% cpu usage where it is 0% on those two for the first few hours where CPU is normal. No events or notifications in the web gui.
Also did all firmware updates on my server as well. Might just have to load 5.5 back on, server ran fine with that version. VMware compatibility list says 6.5 for my cpu but only 5.5 for my server, IBM x3650 M3. Might try 6.7 just to see what happens, this server not in production yet. 😃
I think you are already on the right track.
If you still want to go ahead with 6.7 please check again the HW compatibility list for CPU and Hardware.