I feel like it's not at all weird to say that something is arriving somewhere in that somewhere's local time zone.

More importantly, that's the timezone Mission Control is in. There are no timezones in low Earth orbit because you're orbiting every 90 minutes, so the only timezone that's relevant to anyone involved in the Mission is the one that all the hundreds of ground personnel are using (in Mission Control and to a smaller extent on the recovery ship).

From my understanding, mission control usually doesn't use their own local time. The choice of time depends on the mission, but common choices are UTC or Mission Elapsed Time. The ISS missions use UTC, since the ISS is jointly controlled by Russia and the US, and neither would agree on using the other's local timezone(s), so they use UTC.

Stuff published to the public is not coming directly from mission control, it is being filtered through NASA PR and SpaceX PR. And PR often tries to simplify things for their audience, like converting UTC (which the average person isn't very familiar with) to local timezone. (And sometimes NASA PR also likes to turn metric into US customary, although SpaceX PR does that less.)

The primary target of NASA and SpaceX's PR is American voters, because it is American taxpayer money that pays for all this. Putting things in terms which makes it easier for an American to understand, but harder for a non-American, makes sense in that context.

But, NASA has a global audience. At least have UTC as a secondary time.

Plus, the ISS' timezone is also UTC.

ISS circles Earth every ~1.5 hours, which is ~16 times per day, so it does makes sense to have UTC. Land however is fixed, with its own timezone. I second another answer, local timezone primary and UTC secondary is best.

I agree with local and UTC, as long as both are there. Local is useful for locals, but the audience of a landing is pretty much global.