In the past I would simmer stock without a lid on, and the results were generally good. Strong flavor and good gelling after refrigeration. The only problem is that this resulted in very little stock to make soup out of, so I would have to water it down. Lately I have been trying leaving the lid on while simmering but it doesn't seem to work as well. The stock never gels at all (even when adding chicken feet to my usual chicken bones) and the taste is bland. I cannot see any reason why it would make a difference, but is there some advantage to reducing a stock first and then adding liquid as needed later? Does this extract flavor better?
Basically, a good stock is fairly concentrated. In general, home cooks use too high a water to bones/veg ratio for a proper result. So, when you leave your stock uncovered you are concentrating everything and, perhaps, getting a good result...at least one you like. However, this is difficult to tell without knowing your recipe. With respect to adding water back later, it is not an uncommon practice to reduce a well-made stock further, by half or more, simply for storage purposes. Then when ready to use, water is added to bring it back to the original strength.
I don't see that there's a way in which reducing while making could increase the flavour - less liquid in contact with the bones and more already dissolved in it.
I've always made stock in a slow cooker, so inherently covered. In my new one it cooks down a bit while making, so the bones stick out noticeably by the end even if they started barely covered. The old one was better sealed and I used to always reduce the stock after straining and fat separation (I often still do but sometimes leave it too hot or too long). The end result isn't noticeably different. I don't make it very concentrated, just enough that I normally add some other liquid in cooking.