I think the primary reason would be that landing legs are heavy, and it wastes performance to carry them. If your landing mechanism is mostly on the ground, you get that performance back.
Secondary reasons might include that it's simpler to get the booster right back to the pad. Once things have settled into an operational cadence, it's likely feasible to lower and lock the booster onto the stool, stack a ship on top, refuel, and relaunch -- no more messing around with barges, transport, weather issues, etc.
Your primary reason matches what SpaceX themselves have said. You either need to be strong enough to handle the shock of inpact, or need to spread the impact over time. Building either into the rocket adds a lot of mass.
Landing on a device that spreads out the shock moves that weight to the static landing platform.
It's worth noting that at least 1 Falcon 9 core probably got trashed not from the landing, but from rough seas - so cutting out the ground logistics chain adds resiliency.
To my knowledge, you're right, but in reverse order. I believe the driving force is time, rather than mass overhead, but certainly both play a large part.
Why send the landing mechanism to space when it isn't needed there? Whatever kit you put on a rocket has to be brutally miniaturized to limit how much you eat into the payload mass. Also has to be rugged enough to withstand tremendous vibrations and thermal stresses. That adds cost and more points of failure. You want to move as much of the complexity off the rocket as possible. Then doesn't matter if the catching mechanism on the launch tower is big and heavy.
The rocket equation implies that if you want to maximize the delta-v a rocket gets out of a certain amount of fuel, then you should get the dry mass as close to zero as possible. Eliminating landing legs helps a lot.
The reflected sound of the engines is enough to destroy the engines, ironically. That's also why the launch mount is so high. You'd need truly enormous legs, which wouldn't work for weight.
The load for landing and almost empty booster would be less, but otherwise yes, it would be much more than the single Merlin engine on the Falcon 9, with all associated issues (local scorching/spalling of the pad, acoustic issues, extra weight, longer turnaround, etc.).
You save the mass of the landing systems, you get to have all that mass on the ground and not have to lift it into space. Dramatically improves the performance of the rocket.
1) legs are heavy 2) empty rockets are stronger in tension than compression 3) the booster is large enough to make (1) and (2) matter more than they did for Falcon 9.
