So, something the article mentions is that SpaceX planned for the rocket to explode. That seems odd, why would they want that?

They don't want it to explode, but it is an expected outcome during initial testing like this. Starship is not like any other rocket ever made. It also has very little in common to the existing Falcon 9. Almost all of its design is new and has not been done by any other company. From the steel structure, to the full flow staged combustion rocket engine, an engine design never actually launched previously.

SpaceX operates using iterative design. They build the current design and find and fix issues as they complete it. Once complete they may not even be able to use the specific one they built due to changes in design, but the build teams get extremely valuable experience working with that iterative design and solving issues in the real world.

Most other companies instead spend decades and millions or billions of dollars designing and testing without actually building anything until they have a design they think is final. They then begin to build that model and inevitably discover issues that were never found during design, sometimes requiring large changes in design. See the entire SLS program and subsequent cost-overruns and delays.

In this particular case, it should also be pointed out that the rocket did not explode on the pad, it did lift off. The damage from the pad destruction may have actually been part of the Starship failure, not the Starship itself. The pad structure itself was part of the launch test as well, not just the rocket. The launch caused massive damage to the pad, which was expected and planned for. A water deluge system was planned, but not in place yet. They decided to launch as is to get real world data for what the actual damage to the pad would be. No data existed for what would happen to a launch pad with thrust this high at launch, and the deluge system may not have been enough as designed. No way to know without real world data because it was so far away from any previous tests anyone has ever done for launches. Even the Saturn V, the biggest rocket ever launched, had less than half the thrust at liftoff as the Starship Booster does. The Saturn V had 7.5 million pounds of thrust at launch versus Starship's 16.9 million pounds of thrust.

Very little about Starship has ever been done before. Almost everything related to the vehicle itself, the first stage booster, and the launch pad are entirely new research with very little theoretical research and development, and with almost no real world testing before. SpaceX is not following anyone here. Just like landing rockets for re-use,they are blazing an entirely new trail here no one has done before. And that means there will be failures along the way, they are 100% expected at this point.

The article that this article links to says that the rocket failing wasn't the outcome they hoped for but since the launch was a test rather than a critical mission they spun it as a learning experience. Also apparently the explosion was a deliberate self-destruct after the engines failed partway up, so at least that system works.

They didn’t plan for it to explode. The article is quoting another article that explains that the rocket exploded because they triggered the flight termination system after they lost control of the rocket. It got off the ground just fine, aside from the fact that it’s massive engines obliterated the concrete under the launch mount.

The Starship launch of April 20 was a test for the BFR (Big Falcon Rocket) and Starship. It was considered a major success as it was able to launch off the rocket pad with no major issues (some of the engines did fail on the first stage but the Launch Vehicle was able to continue). One thing to note is the current test of Starship was to launch and possibly test proper separation (which this launch failed iirc). It was never meant to go and complete a full orbit. This launch was the first test of the entire system (BFR and Starship together), so it acts more of "how far can we go with our current progress?"

Almost all unmanned rockets have a faliure mode of exploding, but this is usually done above a safe area. A bunch of debris falling down is a lot safer than a whole Rocket, loaded with explosive fuel. Starship had exploded above the Gulf of Mexico, far away from any pockets of civilization. Keep in mind, to do this launch, they would have to had clearance from government agencies (not sure which one specifically, probably NASA?) to perform said launch.

I guess one major criticism I have of SpaceX's trial and error method is that it does cause more environmental damage than NASA's method (slower development but leads to less lost of vehicles).

Take this with a grain of salt, as I am no means an expert, just an Aerospace enthusiast and am going by what I recall.

Yes it's better to test a real rocket. You can only simulate so much. Also launching into the ocean is by far the safest option. And you need to test the actual pad and the huge launch tower.

Check out the Wikipedia entry for more details.

https://en.wikipedia.org/wiki/SpaceX_Starship_Integrated_Flight_Test?wprov=sfti1