It doesn't take six months to order a new server. You can often have it tomorrow (for some extra fee) or in a week or so. Done this many times since the first ~20 or so years of my career were running our own datacenters.

You're right, hypergrowth (a subset of unpredictable capacity needs) is a perfect use case for AWS or similar.

The vast majority of companies, for the majority of their corporate life, aren't in these categories (spiky, unpredictably) phase though, so for those, AWS is a large cost premium.