Another full-time, long-term college professor here. I believe that this is exactly the correct approach. While we have the availability of a number of software proctoring "solutions" here, I refuse to require my students to install intrusive black-box software on their computers. Nor am I particularly fond of insulting them. One of the things that we forget is that these kinds of measures change the nature of perception of cheating from a moral failure to a kind of hide-and-seek game.
I normally teach face-to-face, and now am trying to cope with hybrid classes (some students online, others facemask-to-facemask in the classroom). Since I am more interested in understanding and application than memorization, the online exams are open-notes and usually open-book as well (since they really need access to property tables). This is not particularly radical, since this is the way that they will be practicing after graduation.
I know that there is at least some cheating going on, but the influence on scores does not seem to be particularly high according to a comparison of score distributions between earlier in-class vs current online results. I am probably a bit naive despite almost thirty years of teaching, but I do believe that students rise to our expectations more often than many believe. And I rebel against a test protocol that tells students that our expectation is that they will cheat.
In any problem, if you find yourself doing an infinite amount of work, the answer may be obtained by inspection.