In the end you save a lot on fuel - you don't need to bring along shielding, life support equipment for the duration of the trip (only expendables and replacement parts).
The trajectory adjustments may be small enough that Hall thrusters, or even just reorienting solar panels or inactive radiators get enough light pressure to make it work. If we are OK with spending a little more propellant, the cycler can be put on a shorter quasi-cyclic orbit that requires course corrections on every pass (IIRC, the shortest trajectory Aldrin considered in his paper would enter Earth's atmosphere, or crust, I don't remember). The cycler maintenance cycles also don't need to coincide with in-transit crews and, in some passes, crews can bring more cargo (or the cycler can dock with autonomous cargo freighters).
If the cycler is large enough, it may have its own food production, so you don't need to carry that too, but then we can also imagine it as a full habitat that's permanently populated and passes by Earth and Mars every now and then and also plants us firmly into science fiction territory. IIRC, the shortest real cyclic path also takes a trip to the Asteroid belt before passing Mars on its way back to Earth. That, I imagine, would be a popular destination for future space colonists looking for resources in the belt to supply passing cyclers.
That would be a killer trip if it includes the belt. I’d pay for that!
But Cyclers won’t save much fuel. Starships (or their descendants) still have to accelerate and decelerate the same, and still need almost as much shielding (a solar flare during descent once you’ve left the cycler is still deadly).
Most of the starship mass isn’t radiation shielding, it’s reentry shielding, tankage, engines, etc.
But once we get to the Cycler stage I think fuel costs will be low on our lists of concerns anyways.
The trajectory adjustments may be small enough that Hall thrusters, or even just reorienting solar panels or inactive radiators get enough light pressure to make it work. If we are OK with spending a little more propellant, the cycler can be put on a shorter quasi-cyclic orbit that requires course corrections on every pass (IIRC, the shortest trajectory Aldrin considered in his paper would enter Earth's atmosphere, or crust, I don't remember). The cycler maintenance cycles also don't need to coincide with in-transit crews and, in some passes, crews can bring more cargo (or the cycler can dock with autonomous cargo freighters).
If the cycler is large enough, it may have its own food production, so you don't need to carry that too, but then we can also imagine it as a full habitat that's permanently populated and passes by Earth and Mars every now and then and also plants us firmly into science fiction territory. IIRC, the shortest real cyclic path also takes a trip to the Asteroid belt before passing Mars on its way back to Earth. That, I imagine, would be a popular destination for future space colonists looking for resources in the belt to supply passing cyclers.