You are confused about who does or should do those things. Cruz should not just flail away in all directions just so you think he is doing something helpful.
Perception is reality. What I think means nothing. Frankly What Cruz thinks means nothing. Cruz's political future is entirely contingent on the perceptions of Texas voters. There are a lot of things Cruz could do to burnish those perceptions and he is not.
While I'm not a fan of the 17th Amendment, it is what stands, and consequently one of the unwritten, implied requirements for a popularly elected senator is sufficient popularity to be elected. Can't sit in the seat without it. Like I said, if Cruz can run to the border to hand out teddy bears to foreigners, he can certainly find time to spend an afternoon in a shelter ladeling soup or handing out blankets to Americans.
So far, the only person Cruz has been helping is his yet unnamed opponent for 2024.
Too late for Teddy to do anything except lay low and hide for a couple weeks.