Indeed, likely the most widespread teaching method today is the Suzuki method, and it doesn't introduce reading until after at least the first couple of years. There are books, but they're more for the parents to follow along than for the kids.

American teachers were horrified by this idea when I was a kid. But the Suzuki method has been successful, and I think it has raised the level of playing overall. Many famous musicians self-identify a "Suzuki kids." On the other hand, many of them admit to not being the strongest readers, but reading takes practice. You can also pick up repertoire by following the sheet music while listening to a recording. Like many skills, it fades if it isn't used. I'm fortunate to be a fluent sight-reader, but not a virtuoso.

In my view the notation is what it is. Changing it would be hard. "Standard" notation creates a kind of symbiosis between composers and players. If a composer uses a nonstandard notation, nobody will play their stuff. And the standardization is why musicians can learn the skill of reading.