At the very least, reducing the number of concerns on the rocket is definitely worthwhile. They are going to have an engine in any case, and using just that and nothing else on the rocket itself simplifies testing and reduces risk. The tower can have a separate testing and there's no way something that happens on the way to orbit and back breaks the tower.
Wings, parachute, etc... All very easy to break or burn at hypersonic speeds, and very chaotic to control. It probably (very probably) wouldn't be possible to land back exactly where the rocket launched on wings or chutes - that would probably need an extremely long and wide runway, but compare the size of Starship to the Space Shuttle... It's like braking a toy car vs braking an actual truck.
The Starship second stage is surprisingly not all that heavy compared to the 78t Shuttle orbiter dry mass, despite the many-fold difference in volume and payload, plus Starship needing to be a legitimate second stage rather than just an orbiter.
Wings, parachute, etc... All very easy to break or burn at hypersonic speeds, and very chaotic to control. It probably (very probably) wouldn't be possible to land back exactly where the rocket launched on wings or chutes - that would probably need an extremely long and wide runway, but compare the size of Starship to the Space Shuttle... It's like braking a toy car vs braking an actual truck.