Mech, I can address your last three points with this: Optics, optics, optics.
You can give, and he can have, rational explanations that would make his trip innocuous, but the court of public opinion will not accept them, and this will be a negative mark on him, moreso by his supporters than by people who hated him anyway. Plus whatever the MSM does with it.
As an example from much, much, lower in fed.gov: I used to constantly have to be the ahole telling our staff that when they were out on ops on our vessels, that they had to leave the surfboards behind. There was actually nothing against gov rules that would prohibit them from surfing on a lunchbreak, or when they were off shift on multi-day ops. However, citizens who saw them just saw gov jackwagons wasting taxpayer money goofing off on their private surfing safari boat paid for by tax dollars. The whole reason we had to curtail it was because people wrote letters and even sent pictures of crew surfing.
On the other hand, the Coast Guard guys could be on their Cutter, parked right next to us, and they could be surfing and no one would say a word. Because the coasties are uniformed, they're out there rescuing people, and the perception was that they deserve breaks like that for all they do. We were out doing enforcement and other stuff people hated, so we had to prohibit all kinds of stuff that was perfectly acceptable and legal because the optics were bad.
This is a case where optics are horrible, and Cruz should have known that (again, if this turns out to be as reported, vs fake news).