Starship as an Aldrin Mars Cycler Component

This week, in lieu of the usual Weekly Space Report, Marcus House has posted one of his “deep dive” videos, this time exploring the concept of a Mars cycler, as proposed by Buzz Aldrin in 1985. A cycler is placed on an orbit which makes repeated fly-bys of Earth and Mars, requiring no propulsion other than to trim its orbit for minor course corrections. High delta-v “taxis” allow crew and cargo to rendezvous with the cycler as it passes each planet, allowing regular interplanetary deliveries. With no mass constraint on the cycler other than that to initially place it into the cycling orbit, it could incorporate shielding to protect crew from cosmic rays en route and a spinning habitat to provide artificial gravity en route.

Starship is the first launch vehicle which, if it works, would make a cycler economically feasible. Could it also serve as a component of the cycler itself?