I think you must have a limited mindset of how long it can take wheels to turn in large companies. Without cloud, it's not uncommon for the F500s I've worked at to take literal months (90+ days) just to provision and stand up a new server for an application team to even begin developing on. Even if you spend time "debugging black boxes" (which is highly debatable), most of the time you're still moving a lot faster with cloud than before.

Some companies are better than others. One place I worked had a decent OpenStack implementation in their own data centers, and it greased the wheels a little bit (though it was not without its own issues). And of course smaller companies are likely more agile and able to move faster. But for the most part, these big companies see some very real benefits in speed by embracing public clouds.

Why don't they give the application team a few extra servers to do whatever on without asking for permission?

Because without good organizational controls, the developers will put those servers into production with no HA, backups, and insecure configuration.

I’ve seen it multiple times in my careeer.

That makes a lot of sense. I can see how using cloud solves for HA and backups. But how does insecure configuration come in?