Then why isn't anyone running an AWS-like service focused for bandwidth-intensive applications hosted on "OVH, Hetzner, etc..."?

Many people do. S3 is convenient though. It handles durability, replication, uptime, etc... and even with the insane markup on bandwidth many startups / companies can afford a $10k/mo bandwidth bill because it's cheaper than hiring some devops and a team to build out the appropriate infrastructure.

That's what I meant with "really cheaper". Sure, bandwidth costs are lower with Hetzner, but that's not everything.

It depends on how you define AWS-like services. Lots of VPS providers cater to bandwidth-intensive applications and are hosted on cheap dedicated servers.

But you don't have to store and serve all the content from Amazon or your own platform. You can easily set up aggressive caching, in a network you control, backed by S3.

And you pay premium for premium bandwidth. You can't just assume that all your users will have a good experience if you buy hardware and bandwidth from the cheapest providers around.

Amazon bandwidth isn't particularly premium. It's just expensive.