Actually, this kind of HDMI switch (that is "always negotiated") does exist. This page has a very nice article about HDMI and the troubles of "handshaking":
Since we do power-off displays and source devices most issues occur
when these devices are powered on again to re-negotiate the HDCP
handshake between source and display.
...Some displays may also re-negotiate the handshake when swopping to
another input e.g. AV1 ,AV2 or another HDMI Port (wait 10 seconds) and
swopping back to correct HDMI Input via remote control.
Some devices such as switches and HDMI Switches / Combo splitters also
allow for HDMI handshake re-authentication by switching from one input
to another and back to the input having HDCP handshaking issues.
The "thing" that keeps the "handshake" open is called EDID - that is, *E*xtended *D*isplay *I*nformation *D*ata. See here:
Extron HDMI matrix switchers also feature Key Minder®, an
Extron-exclusive technology that continuously verifies HDCP compliance
for quick, reliable switching.
Octava has this to say about EDID:
-EDID Management: EDID is an acronym for Extended Display Information Data. EDID was originally implemented by computer monitors to
communicate its display capabilities to the video card so a compatible
video resolution could be negotiated. EDID is also used by HD Displays
via HDMI to identify the HDTV display and audio capabilities to the
connected video source. Basic HDMI switches with single output simply
pass the EDID directly from the display to the source. For multiple
output devices such as a HDMI distribution amp, or matrix switchs, a
method for customizing or managing EDID is recommended. EDID
Management allows the user to manually select the desired EDID in
order to properly operate a multi- display system which may include
multiple displays and audio receivers each with differing capability.
EDID ... It is what enables a modern personal computer to know what
kinds of monitors are connected to it.
Here is an example of an HDMI Switch that uses EDID:
This 1X4 HDMI Splitter w/User Adjustable EDID chip-set includes a chip
to makes sure the sound and the picture are in sync and no delays
occur between them.
However, it seems that the ports have nothing to do with licenses, really, however, the switch must be HDCP compliant, which is where the notion of "license" may have come from.
The reason it seems like the devices have to "re-register" is because the switch does not maintain continuous EDID communication with the sources. To have the seamless integration, the switch has to have a EDID control inside which can "know" that devices are still connected by detecting their display settings.