This is a good question. It’s important to have a pre-TRT baseline measurement otherwise you will probably never know why it ends up low after starting because you could never rule out the testosterone being present and/or changing your body even if you were to stop.
I had low SHBG before TRT, and I had the beginnings of metabolic syndrome. I wasn’t too overweight and my glucose and A1c looked great. But I had subclinical hypothyroidism and my fasting insulin was very high. Cholesterol was horrible as well. Fixed those and SHBG went from 8-10 to 23.
Another reason as Cataceous pointed out could be due to SHBG being a regulator of sex hormones. You could see a drastic swing, but as he said you would probably need something like Estradiol being undetectable for something like that to happen. I have not seen a TRT dose tank SHBG in its own without something else being involved. It could also be caused by medications or simply genetics.
I don’t feel testosterone anymore regardless of where my SHBG is at, but that’s because better has become my normal and it no longer feels different or new. Testosterone does not fix a lot on its own for me specifically, but that’s because of the Accutane I was given as a teen, not SHBG’s fault. I have very little 5-ar activity happening. So I work on keeping DHT high and supplementing that with other androgens which makes a huge difference.