I feel like this is similar to the argument about mounting a optic on the carry handle and how high it is. It's something you'll notice a million different wrongs when you're at home playing with it but once out in the field, it's a non-issue.
Yes, sometimes at home I can see the FSB if I concentrate hard enough. I can see a small black "blob" on 4x. At 1x, the post can be seen. It doesn't bother me too much.
However, if you want to shoot at close range, and your particular optic has illuminated reticle, maybe learn the occulted shooting technique. A good way to do this is to have a cap or tape that you put over the front of the sight so you can't see anything out of it. The idea is you use both eyes and so long as you keep both eyes on the target, you can interpose the dot from the optic over the target. You can do this with any optic, no matter the magnification so long as it is illuminated in some way.
Trijicon calls it the Bindon Aiming Concept and Armson still makes the OEG reddot that's sort of still useful amongst today's optic field.