You can build a sandboxing language without any sort of stack walking. SEL4+C does this. It doesn't have especially good usability at scale, and it's not easy to modularise.

You're imagining a system where there's no specific authentication system for code. Instead in order to use a library, you need to explicitly and manually obtain all the capabilities it needs then pass them in, and in main() you get a kind of god object that can do everything that then needs to be progressively wrapped. If a library needs access to a remote service, you have to open the socket yourself and pass that in, and the library then needs to plumb it through the whole stack manually to the point where it's needed. If the library develops a need for a new permission then the API must change and again, the whole thing has to be manually plumbed through. This is unworkable when you don't control all the code in question and thus can't change your APIs, and as sandboxing is often used for plugins, well, that's a common problem.

There's no obvious way to modularise or abstract away that code. It can't come from the library itself because that's what you're trying to sandbox. So you have to wire up the library to the capabilities yourself. In some cases this would be extremely painful. What if the library in question is actually a networking library like Netty? There could be dozens or hundreds of entry points that eventually want to open a network connection of some sort.

What does this god object look like? It would need to hold basically the entire operating system interface via a single access point. That's not ideal. In particular, loading native code would need to also be a capability, which means any library that optimised by introducing a C version of something would need to change its entire API, potentially in many places. This sort of design pattern would also encourage/force every library to have a similar "demi-god" object approach, to reduce the pain of repeatedly passing in or creating capabilities. Sometimes that would work OK, other times it wouldn't.

The stack walking approach is a bit like SELinux. It allows for a conventional OO class library, without the need for some sort of master or god object, and all the permissions things need can be centralised in one place. Changes to permissions are just one or two extra lines in the security config file rather than a potentially large set of code diffs.

Now all that said, reasonable people can totally disagree about all of this. The JVM has been introducing more capability objects with time. For example the newer MethodHandle reflection object is a capability. FileChannel is a capability (I think!). You could build a pure capability language that runs on the JVM and maybe someone should. Perhaps the usability issues are not as big a deal as they seem. It would require libraries to be wrapped and their APIs changed, including the Java standard library, but the existing functionality could all be reused. The new libraries would just be a thin set of wrappers and forwarders over pre-existing functionality, but there'd be no way for anything except the god object to reach code that'd do a stack walk. Then the security manager can be disabled, and no checks will occur. It'd be a pure object capability approach.