Its more pressurisation cycles which kills the TP's.
Anything less than a 30-40 min sector tends to increase your capital usage cost for the flight above what it should be. Also there tend to be life'd items due number of landings on retractable gear.
The actual starting and stopping of the engines doesn't really come into it apart from an increase in the number of starter gens you go through and battery's if your not doing GPU starts. There is no record in the techlog of starts only of landings and airborne hours.
And there might not be an option on the tri's anyway because the report is out now for the one that blew an engine. And there are several safety items that need addressed in regards to the engine out performance.