The problem with being sent over the threshold is in case of a missed approach. You could be right in the way....
However. Other airports seem to manage it with no loss of seperation. LAX for example.
It is a British disease that tries to seperate GA and CAT. Many other parts of the world seem to be able to combine all types of air user without too much difficulty. In just as busy airspace as we get here.
I'm in no way saying that it is easy to do it, but here in the U.K you can often say that nobody even tries. That is what I find hard to swallow.