Having used KVM's for many years I've found that the definitive
answer, at least for the 'budget' range of KVM's, is it's down to the
motherboard how well ( or bad ) they work with KVM's. I've had systems
that will only boot if the KVM is switched to them and others that
only boot if it isn't. Then there are those that boot differently
whether switched or not, and that can be a whole range of things from
hanging at a different phase of the boot cycle to the OS failing to
start up correctly, or the graphics resolution to be different.

Also found that the quality of the KVM cables makes a huge difference
in boot reliability too, and it's not always the more expensive ones
that work better !! One set I had worked a lot better after wrapping
the entire length with kitchen foil - evidently a lack of screening
here - they aren't used any more

Perhaps a more up market KVM would be less problematic but whilst the
budget range does the job I'm happy to live with their foibles