There would be no drawbacks to adding a safer API, but designing an improved API is time consuming as you state yourself. You want to carefully consider new API as once they are added, they can "never" be removed. This also means that the existing unsafe API would have to stay, but could be deprecated. Likewise the new safe API would likely be a wrapper over the existing unsafe API, not a complete reimplementation.
I think each iOS release increase the major, minor or patch version of the Foundation framework that ship with that version of the system, bumping the framework version is not a problem, the problem is that you want the Foundation framework to remain API and ABI stable.
API Stable
Remaining API stable is not particular hard, new functions etc. can be added to all structs, classes and enums, but you can't remove function or method calls, or change the return type of a function etc.
If the foundation framework were to break API stability in release X.Y.Z, then all existing code would have to be updated to work with release X.Y.Z, they would have to make extra work to remain backwards compatible with previous releases, and they would have to be recompiled.
I believe Foundation does break API every once in a while, but not often. The only case I can think of is when they remove API that have been deprecated for years and years. The Swift standard library have also broken API in earlier releases.
ABI Stable
Remaining ABI stable places some hard limits on what you can change in the frameworks code. Adding a new instance variables to a struct is ABI breaking, even if it is private. Using a class gives you more freedom to make changes, but you could likely still get into issues if part of the code has been marked as @inlinable. Swift enums support adding new cases in an ABI stable manner, but that is an API breakage I think.
Having Foundation framework break ABI would be highly problematic for consumers of the framework, because it ships with the operation system. If you write software that uses Foundation (or any other code that ship with the OS like the Swift Standard Library) and it had an ABI breakage in iOS release X.Y.Z then you would have to decide to either write your software to work on iOS version X.Y.Z and forward, or all versions before release X.Y.Z. You can't write software that can run on both.
I don't think Foundation have ever had an ABI breakage, and it likely never will. This is also the reason that (almost?) all structs in Foundation and the Swift standard libary is @frozen to highlight that making ABI breaking changes is not an option.
As a final disclosure, take everything above with a grain of salt. I am not an expert on API and ABI stability, some of this might be incorrect or slightly misleading.