The long term key is dependent on the principal's password.  Therefore,
which long term key used depends on the principal running the service.  Any
services running as local system will use the computer accounts long term
key; any services running as another principal will use that principal's
password as the long term key to establish a session key.

In the case of your example, a new ticket is needed for each SPN.  Even
though you and your computer have proved your identity, you still require
tickets for different services as those tickets are for a specific service
and not a generic catch all for a specific system.