If you see range that's in a normal range, you'll apply.
Also for higher end salaries, the hiring is done differently and the expectations are generally different on both sides of the negotiation. You pretty much NEVER hire a $360K-$2M by putting out a req. You may do that as a formality but there's zero expectation of getting anything useful.
I once worked for a company that round-filed every Job Board and mailed resume application as a matter of SOP - they ONLY hired if an employee or trusted collaboration partner recommended the person. They created an EEOC-compliant process for legal appearances but they never hired through that.
Higher salary positions are more the same only more so.
Edit: the other factor - most jobs (I've seen claims of 80%) don't exist before the "right candidate" has already been found. I.e. the position is created for that person and not vice versa.
So I can kinda see how not advertising above the normal probably allows them to attract decently skilled folks who might not normally apply for a 200k+ job, and they might actually be better. And of course for the applicant when they get that healthy offer they didn't expect everyone wins.