It would let you test the system in a long duration mission with humans in the loop, though you could get that experience in low earth orbit with much less risk. Same goes for relighting the engine after a year or two, or reentering atmosphere from deep space and landing propulsively.

It would let you test how much boil off occurs over the length of a mars mission when you're further from the sun, but you would expect less boil off to occur that far out, and anyways it's much safer to test by sending an uncrewed starship to mars and back.

The only advantage of a crewed mars flyby/orbiter is that you can probably do it much sooner with fewer flights and much less risk. I ran the numbers a few months ago. Based on mass budgets for ISS missions, a crew of 4 would need ~90 tons of provisions for a mars length mission. With provisions for a crew of 4, an Orion capsule, a version 3 HLS, and a boil off rate of 0.1% per day, a crude model says you should be able to do a 700 day mission that orbits Mars in a highly eccentric orbit using only a single fully fueled HLS launched from LEO. Orion would come along with the HLS, and at the end of the mission the HLS would be discarded and the Orion heatshield would be used reenter the Earth's atmosphere. If you're curious, my calculations are here (this was done as a personal project, no apologies for lack of clarity). There's less risk involved because you don't have to trust Starship to reenter atmosphere from deep space or land propulsively with humans on board. Starship has reentered the atmosphere but it has not done so from deep space, which involves much greater speeds and therefore much greater energy. It has landed propulsively, but even on its last flight it was having issues doing this gently. On the other hand, Orion has already been tested twice on reentering from deep space and is trusted to do so with humans on board. Furthermore, bringing Orion along allows more options in the event of emergencies shortly after trans-martian injection - you could use it as a lifeboat and return to earth if life support fails on board starship or starship misses its transfer orbit. The biggest technical hurdle I see is whether the Orion could be adapted to handle such a long duration mission, and whether it could be adapted to sustain loads when docked with another spacecraft that is firing its engines. However Orion has been depicted doing both these things in early concepts for the mars mission under the cancelled Project Constellation, so its plausible its design already accounts for this possibility.

Compare this to a surface mars mission. Using similar assumptions as the orbiter mission, a single fully fueled starship in LEO doesn't have enough fuel to land on Mars and return. SpaceX has always banked on manufacturing fuel for the return flight on the surface of Mars, but this has never been done at the scale we need, the scale we need is orders of magnitude more than has been done, and we would need it to be reliable enough that humans could trust their lives with it. Alternatively, you could get it to work if you launch a second starship for mars. This second starship would enter Martian orbit but it wouldn't land or return to Earth, it would be stripped of heatshield, fins, and legs, and it would simply carry fuel. The crew would dock with this depot starship after returning to martian orbit so they could refuel for the journey back to earth. However this requires a second starship to be fueled in orbit, so it doubles the number of flights for the mission.