Any project may change at any time. That's why they bump from v1 to v2. But by not using the full precision of the version number, you're not able to communicate as clearly about releases. A minor release may not be 100% compatible with the previous version, but people still expect some degree of similarity such that migrating is not a difficult task. But going from v0.n to v0.(n+1) uses that field to communicate "hell, anything could happen, YOLO."
By releasing a library with version 1.0, I communicate: "I consider this project to be in a state where it is reasonable to depend on it".
By releasing a library with version 0.x, I communicate: "I consider this project to be under initial development and would advice people not to depend on in unless you want to participate in its initial development".
I don't understand why people find this difficult or controversial.
For example, sometimes projects that have a 0.y version get depended on a lot, and so moving to 1.0.0 can be super painful. This is the case with the libc crate in Rust, which the 0.1.0 -> 0.2.0 transition was super painful for the ecosystem. Even though it should be a 1.0.0 crate, it is not, because the pain of causing an ecosystem split isn't considered to be worth the version number change.
99% of the time this situation is okay, because Cargo allows you to have both 0.1 and 0.2 in the same project as dependencies. It's just packages that call out to external dependencies, like libc, where it enforces the single version rule.
Most of the time, it works so well people don't even notice.
The only time you run into a problem is if you try and use values with a type from 0.1 with a function that takes a 0.2 as an argument, or whatever. Then you get a type error.
Nobody cares that Chrome's major version is 147.