I recommend you try it once ;) you will often find that the remaining soggy husk of the vegetables you started with negatively affects the overall dish.
If you boil it for long enough some vegetables will eventually dissolve, but many brake down leaving fibrous and comparatively tasteless remains.
Much flavour is stored in the fats and lipids and other liquids within the vegetables or otherwise between the fibers, the general mechanism in creating a stock is to raise the temperature to a point where these can be dissolved out of the vegetable and then we want to separate the flavour from the fats themselves and extract it into the liquid, thus physically removing all these elements from the original produce.
Think about it from a mechanical point of view, the raw vegetable is made up of these tiny packages of flavour, these packages are then stored within more layers of tight packaging, the stock process has to break apart all those tiny packages to extract the goodness, what it leaves behind is simply a mess of shattered packaging materials.
Onion and celery are really good examples, even when the final dish expects these elements and you are creating this stock specifically for this dish, you would remove what remains of the stock base ingredients and add in fresh vegetables for this dish itself.
Try it once, this is an art form after all. In certain dishes, it may add a desirable texture, but it is not usually so.
Keep in mind that if you are preparing your stock to store for later that the fibrous material left behind will provide a safe harbour for bacteria to form and multiply, it creates temperature differentials and the organic material will start to rot causing the rest of the liquid to spoil much sooner than it would have if you had sufficiently filtered it first.