You work out the minimum requirements and write to that, you don't start out with the latest and greatest and work backwards.
FE having a specific way of working, doesn't preclude that way being broken.
"That some field (e.g. FE) has a specific way of working is orthogonal to that way being broken or not".
Otherwise there would never be any brokenness conceivable ever, and everything would be a matter of different ways/conventions.
I don't see why brokenness shouldn't be a possibility in FE or anywhere else though. Sure, I might be wrong, and FE might NOT be broken. But that would not be the case merely because "it has its own way for doing things" -- it would have to be inherently not broken, whereas "has its own way" merely tells us that it's idiomatic.
You start with the damn requirements and then look at how the application may need to be built.
The latest browser APIs are not useful for 99% of the FE work going on out there. Yes, I know it's more satisfying to pretend that it is important, but it really isn't. Just because you can hook something up to a users webcam, or post annoying browser notifications about the latest cat picture a user uploaded doesn't mean you need to or even should.
FE is not a special snowflake. It's no different from most software development (and yes, other, non-FE developers have to figure out cross platform issues as well). If you want to be taken seriously in software development, then stop with the unprofessional attitude and learn how to do something useful for your users, like <a href="https://en.wikipedia.org/wiki/Progressive_enhancement">Progr... enhancement</a>.
the alternative you propose is that everyone writes code that only targets well-supported javascript, but does that exclude polyfills or convenience functions? Does that mean that using a polyfill for Array.prototype.map is worse than using an implementation like _.map or a hand-written map function? At best, this choice results in a complex maintenance burden that is borne by developers during future refactors (rather than an infra-focused developer upgrading the babel distribution and its presets/plugins)
the current reality is that the browser ecosystem remains heterogenous (which is why there is still a valid market for things like jquery). A plugin like babel-preset-env for instance allows you to dynamically adjust the "minimum requirements" without needing to write new polyfills and gives the benefit of improving the transformed code with little to developer intervention. It's computers doing what they're good at, i struggle to see the harm in that.