> As a complete lay person with little to no physics knowledge: what stops the use of something dumb like a parachute, or even wings and landing gear, to "land" the booster?

The main advantage is that you don't need to spend any of your payload mass budget on a parachute, or wings and landing gear. The secondary advantage over a parachute is that you don't need to fish it out of seawater and make your refurbishment process more of a pain in the ass.

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.

It mostly comes down to reducing extra weight. You have to carry those wings and landing gear upwards, which reduces useful payload weight. But having the booster right where it started also helps with reusability. No need to transport the booster from a landing strip back to the starting table

physics?

Parachutes give little or no control over where and how the rocket lands, are unreliable (unfurling fabric behaves chaotically; modern spacecraft still don't have 100% reliability on their parachutes), and are surprisingly heavy.

Wings and landing gear are useless extra weight during launch, and excess weight on the booster has a super-linear reduction weight delivered to orbit. (the Tyranny of the Rocket Equation)

During the 1960s, NASA investigated using inflatable Rogallo Wings (basically hang gliders) to land the Gemini capsule. It worked fine, but was more complicated than parachutes, and re-use was not one of the goals of the Gemini or Apollo programs.

None of those give much margin for error on landing. Without any kind of propulsion, there's no option to come to a hover or do another go-around if the landing isn't going well. Space Shuttle pilots had to do extensive training in simulators for the landing because they only got one shot at it during the mission.

Propulsive landing doesn't require any hardware that isn't already on the launch vehicle, only a little excess propellant. (And it is a small amount; Super Heavy is like a soda can that's full of liquid at launch and only has a swig at the bottom during landing.) Propulsive landing gives Falcon 9 and Super Heavy the ability to overcome wind and other weather conditions to make pinpoint landings. Engine throttling gives Super Heavy the ability to hover, so it has a huge margin for error when coming in for a landing.

Super Heavy could have had legs, like Falcon 9, but it has such a huge payload capacity that they can simply choose to always launch with enough propellant to come back to the tower, and it saves a lot of flying weight and complexity by simply not having them. The arms on the tower can be massively overbuilt to ensure however much reliability SpaceX wants.