This is just my 2 cents on this question...not sure if this holds true in its entirety.
Each Object has a monitor and waitset --> set of threads (this is probably more at OS level). This means the monitor and the waitset can be seen as private members of an object. Having wait() and notify() methods in Thread class would mean giving public access to the waitset or using get-set methods to modify the waitset. You wouldnt want to do that because thats bad designing.
Now given that the Object knows the thread/s waiting for its monitor, it should be the job of the Object to go and awaken those threads waiting for it rather than an Object of thread class going and awakening each one of them (which would be possible only if the thread class object is given access to the waitset). However, it is not the job of a particular thread to go and awaken each of the waiting threads. (This is exactly what would happened if all these methods were inside the Thread class). Its job is just to release the lock and move ahead with its own task. A thread works independently and does not need to know whihc other threads are waiting for the objects monitor (it is an unnecessary detail for the thread class object). If it started awakening each thread on its own.. it is moving from away its core functionality and that is to carry out its own task. When you think about a scene where there might 1000's of threads.. you can assume how much of a performance impact it can create. Hence, given that Object Class knows who is waiting on it, it can carry out the job awakening the waiting threads and the thread which sent notify() can carry out with its further processing.
To give an analogy (perhaps not the right one but cant think of anything else). When we have a power outage, we call a customer representative of that company because she knows the right people to contact to fix it. You as a consumer are not allowed to know who are the engineers behind it and even if you know, you cannot possibly call each one of them and tell them of your troubles (that is not ur duty. Your duty is to inform them about the outage and the CR's job is to go and notify(awaken) the right engineers for it).
Let me know if this sounds right... (I do have the ability to confuse sometimes with my words).