Pilot reported loss of engine throttle control during flight back to home airport. Flight crew continued and landed safely.

Narrative

On return home from a routine training flight the pilot flying (myself) noted a loss of throttle friction as well as inability to change manifold pressure. The pilot not flying (PNF) was an experienced pilot and the two immediately started to formulate a plan. The power setting was more than adequate to maintain straight and level flight. I flew to a training area making sure to stay outside of controlled airspace. Analysis of the situation determined that the most likely cause was a lack of connection between the throttle cable and carburetor. There was no checklist for this malfunction. We performed a controllability check and determined we were able to fly a roughly 3-4 degree glide slope with the gear and flaps down and prop full coarse. After that; we (myself and PNF) agreed on the plan and the PNF started talking to ZZZ Tower to coordinate and [request priority handling]. CRM between the crew and ATC was excellent in my opinion. ZZZ Tower cleared the longest and widest runway for us and ensured no aircraft conflicts while we flew a normal straight in. Since I was unable to set the throttle to idle to stop on the runway; I shut down the engine just prior to touchdown and rolled the airplane to a stop uneventfully. Rescue crew and equipment were ready and waiting. We terminated the [priority handling] and towed the airplane back to the hangar.Upon inspection it was clear that the throttle cable had become separated from the carburetor. There is a threaded insert that holds the throttle cable to the carburetor. This was gone. The locking feature which retains this threaded insert had failed in flight and allowed the threaded insert to back out and the throttle cable to become disconnected from the carburetor. This was the root cause of the issue. While we can never be 100% certain what locking feature was in use at the time it probably was not to specification. The original design uses a hardened metal pin which will not wear and fail in flight. For the repair; an original specification threaded insert was re-installed and the original specification pin installed to ensure this does not happen again. Fit check; inspection and engine run were performed afterwards to confirm normal operation.