I'm not sure I've ever said it's "not possible", because of course it is. But the TD wasn't designed to do this, and it would be a pretty huge undertaking to make it work. I'm always about balancing the cost of a feature with its benefit. The cost usually means how difficult the feature will be to implement, how much of my time it will require, and how much it will impact other features. Benefits includes not only how much of a benefit it provides, but also how much of the TD's audience will find the feature beneficial.
Something like this has a huge cost, since it hits pretty much 90% of the application. It would likely take me months to complete, and I'm not even sure how some of it would work. I would likely be working on nothing else, so all other work on the application would have to be halted. So: very large cost. On the benefits side, I can see how this would be a really big benefit ... for some people. In fact, the audience for this is pretty small. I only know of a handful of users that would benefit, and extrapolating from that would probably (I'm guessing) mean that perhaps dozens of users would benefit from this. In the grand scheme of things that is a very small audience. So in this case the cost greatly outweighs the benefit.
Opening another window with a clock in it would likely be the easiest part of the whole concept. All of the Settings window tabs are designed for a single tournament. It's not only a coding issue, but a design issue.
OK, having said all of that, version 3.3 will have a way to run more than one instance of the software at the same time. Because the database, data store, and preferences aren't designed to work concurrently, it won't be able to run concurrently by default. You'll have to start the software using a special flag. And keep in mind that there's a potential for data loss regarding those items I just mentioned.