It often isn’t convenient, no. There is another approach which you might have considered. Apply the 'filter' to each object that needs it as a MeshEffect.
This only works for some sorts of filters. But if it works it is in theory more efficient, as it avoids drawing everything twice, once into the filter and once the texture after filtering.
It can increase your number of draw calls, which can affect performance in another way. But it then becomes an optimisation problem which is often easier to work on.