If you lower your e2 on trt with an ai will shbg go down with it. I know both these hormones need to be at the same level for good sexual function.
SHBG is release by the liver to scavenge steroid hormones for removal/metabolization by the liver. The more E2 you have, the higher SHBG will go. More T lowers SHBG. So there is a tug of war going on. SHBG levels seem to be slow to respond, so changes will not be immediate when E2 is lowered. But when E2 is lowered from higher to near E2=22pg/ml, one can feel a huge difference in one week - at least for almost all guys.
SHBG can be affected by some drugs and some medical conditions and indirectly by drugs that interfere with E2 clearance in the liver that leads to higher E2 levels. So the situation is not as simple as it often appears in ideal cases.