Roy Fielding, author of the HTTP specification, disagrees with your opinion, that CSRF is a flaw in HTTP and would need to be fixed there. As he wrote in a reply in a thread named The HTTP Origin Header:
CSRF is not a security issue for the Web. A well-designed Web
service should be capable of receiving requests directed by any host,
by design, with appropriate authentication where needed. If browsers
create a security issue because they allow scripts to automatically
direct requests with stored security credentials onto third-party
sites, without any user intervention/configuration, then the obvious
fix is within the browser.
And in fact, CSRF attacks were possible right from the beginning using plain HTML. The introduction of nowadays technologies like JavaScript and CSS did only introduce further attack vectors and techniques that made request forging easier and more efficient.
But it didn’t change the fact that a legitimate and authentic request from a client is not necessarily based on the user’s intention. Because browsers do send requests automatically all the time (e. g. images, style sheets, etc.) and send any authentication credentials along.
Again, CSRF attacks happen inside the browser, so the only possible fix would need to be to fix it there, inside the browser.
But as that is not entirely possible (see above), it’s the application’s duty to implement a scheme that allows to distinguish between authentic and forged requests. The always propagated CSRF token is such a technique. And it works well when implemented properly and protected against other attacks (many of them, again, only possible due to the introduction of modern technologies).