Why would management care about tools?

In the first example, they didn't and recruited a CTO who made a tool choice that arguably killed the business (maybe it still ends the same with PHP, minus the experience of building a nicely architected system in Perl: what-ifs all around).

Management does need to care to ensure they hire people who will make the right choices (which is a careful balancing act of investment vs returns) if they don't trust themselves to do it.

Exactly, when they do its a sign of bad management. The only case I can think of when this isn't true would be the difficulty in finding people willing to use/work in that language. But in all but the most obscure languages, this is probably given too much weight by management.