So, you can just let your medical lapse, hop in a light sport elligible plane, and if the FAA comes calling, just say you are operating under light sport privileges? You don't need to file anything with the FAA letting them know you are transitioning?
That's right. Once you earn a Pilot certificate you keep it for life unless you voluntarily surrender it or have it revoked through an administrative action (enforcement).
You have all the privileges of that certificate AND lesser certificates, provided you meet the requirements to exercise those Privileges.
For example, I hold a commercial pilot certificate, airplane single and multiengine land, instrument airplane.
As long as I have a second class medical I can exercise my commercial privileges.
As long as I have a third class medical I can exercise my private privileges. I don't HAVE to renew my second class medical.
If I let my medical lapse, I retain sport pilot privileges.
I must have a current flight review for all levels.
My instrument privileges depend upon my medical and my instrument currency. My passenger-carrying privileges depend on my recency of flight experience.
Through all of this, as far as the FAA is concerned, I'm a commercial pilot.
The only certificate I have that requires renewal is my CFI.