It very much depends on how code is written. A typical LAMP (style) stack wouldn't be any better on the cloud than it would on shared hosting. But if you can make use of serverless (eg lambda, S3 and/or DynamoDB on AWS) then that's where you'll start seeing some advantages.
https://murex.rocks is a static site that costs me pennies each month and has zero scaling issues. The site is fully automated too, built from CI/CD (Markdown converted to HTML) upon commits to a master git branch. But it was purposely designed to run on the cloud.
This isn't to say that shared hosting isn't a worthwhile option, just that cloud can be cheap albeit you do need to architect your project for using the cloud rather than lifting and shifting your existing LAMP stack and expecting that to behave the same.