SpaceX

There's two main benefits: faster reuse and more payload to orbit.

A Falcon 9 landing on a drone ship needs to be transported back to shore. That's multiple days before the engineers even get their hands on it to prepare for the next flight. The design goal of Starship is to launch a Ship into orbit, return to the tower, be restacked, refuelled and launched again in the same day. Will they actually get it to the point where that's possible? Remains to be seen. Until now, they had no way to see what real stresses a Starship booster goes through in a flight. They're gonna rip this one apart down to the spacers in its bolts to examine it. With the flight and physical inspection data, they'll make what improvements they can to the already built boosters and design future boosters to be more resilient. SpaceX has, by now, a well proven track record of doing what others think is insane to even attempt. If anyone can launch the same rocket twice in a day, there's no one better to give it a try.

The increased payload comes from not having the mass of the landing legs. The Falcon's landing legs weigh several tons. Starship, being 3x the diameter and 10x the mass, would need titanic landing legs. That's a lot of tonnage you won't be taking to orbit. Catching on the tower means that all but a fraction of the landing hardware's mass isn't on the rocket itself. As an additional benefit, the landing hardware needs to be built only once. Every Falcon has its own landing legs, but every Starship they ever build could land on the one tower they have now. That won't be the case, they're planning to build multiple towers, but the sentiment remains the same.