The Windows (and, for that matter, Linux) security model generally holds that everything a user (in the "login account" sense) does is done at the same trust level. In other words, any two processes running with an identical security token are trusted exactly the same amount. If one process can access its own memory (which of course it can), so can the other.
If an attacker has arbitrary code execution on your account, it's already game over. Even if you don't let them access the memory of current processes, they can launch processes themselves under a debugger, overwrite scripts/libraries/executables stored in user-writable locations (such as your login/shell resource scripts), read or write all the data that a program running as you would have access to, and so on. In other words, there's very little value in creating a security boundary between a user's processes.
Now consider the advantages of not doing so. You don't need to be admin/root to debug a running process, which might be in a weird state that would be hard to re-create. You can write tools that modify or extend the functionality of programs installed in non-user-writable locations (this is heavily used in game modding, for example). Basically, you - the user - have more control over the software running on your session, and you can do it without needing elevated privileges. The only cost is that there are a few new ways that somebody an attacker running code as you can hurt you, and at that point, they don't really need any more.
Windows' Process objects do have ACLs, which can be used to do things like give another user access to your process' memory or allow certain access (such as the ability to tell when the process exits) without other access (such as the ability to write to the memory). You could also restrict the access to a process from its own user - the same way you can restrict access to a file you own - but the owner of any object can overwrite its ACL so another process also running as you could just overwrite that restriction (again, like marking a file you own "read-only").
In general, if you want to ensure other processes cannot tamper with a process you launched, you need to launch it as another user. There's a few ways to do this, such as
CreateProcessWithLogon or creating a Windows Service. The Win32 API does not provide an equivalent of the "setuid" bit on a file, but a privileged service account can emulate that behavior. If you want to restrict what an app can do, you can easily create a low-privilege version of your own security token with
CreateRestrictedToken and then create a sandboxed process using it (an open-source example of this is the Chrome sandbox on Windows).