How does a cdn makes you backend faster or your latency better ? I thought it was only for distributing static assets and managing DDOS. If it is for cachable but dynamic content install reverse-proxy cache it will fly.

Because it lets you use it as a geographically distributed cache basically. Most GET requests should be able to be cachable on the typical website, besides the ones that are unique per logged in user or similar.

If your server is in Europe, and you have Australian users, there is a physical limit how low the response times can go, serving bits over that distance, so only way you can make it go below that limit, is by moving where you serve the data from closer to the user.

Lots of websites have horrible performance for whatever reasons, and lots of freelancers/consultants basically default to throwing a CDN on top of those when they get approached by businesses to fix the slow website browsing, as they're not the ones who have to pay the monthly subscription, and the less work they have to do, the better $ per hour spent for them.

I agree that it's a shit solution and there is much better sustainable ways of solving these things.