If you built a website 20 years ago and it exploded in traffic, shared hosting without easy scaling would not be a solution. You would have to plan your growth and pre-order shared instances. Thus making your business cash dependent again without proven growth.
Google ran for many years on piles of commodity boards and they were expanding pretty fast...
The amount of marketing hype around cloud services is insane because all the big tech companies have a vested interest in your renting their platforms. It doesn't allow you to do anything you couldn't 15 years ago, just makes it easy.
Plus, the level of resources for configuring EC2-like servers, and Heroku-esque preconfigured servers reduce the barrier to entry pretty significantly.
You could host a reasonably successful web site on a relatively low end server (say, a Sparc 10) off a T1 line (1.5 megabits) and serve a ton of users. They all had crappy connections and were used to waiting.