Based on what you wrote, it seems Columbia is a no brainer - because your cons are - well, if they matter to you they’re important - but do you really think you wouldn’t be free to speak at Columbia? You have to take those things with a grain of salt.
While I get it and have argued - someone who wanted a top 10 school got ripped off by the lying - but do you think Columbia is any less respected than 3 months ago and 3 years ago? Do you think anyone professionally is looking at that and saying - Columbia is a bunch of liars, let’s go to Stony Brook?
On the flipside, yes, there are many with physics degrees who get engineering jobs. And the stats say 75% of engineering majors or engineers don’t work in engineering. My son’s internship this summer wanted engineering students and yet the job wasn’t engineering as it turns out. I asked why then all the engineers? Because they want people who think like engineers.
Choose the right school for you based on the schools - not societal nonsense (IMHO it is) like your Columbia cons that won’t impact your day to day experience.
Good luck to you.