The free hormone hypothesis is indeed a myth and based on very old studies with limited in vitro tissue samples. However, that's true for most hormone research.
In men on TRT, low SHBG will increase free diffusion through cell membranes, but accelerate hepatic metabolic clearance and reduce intracellular and extracellular AR signalling. In one study, for example, human androgen dependent prostate cancer cells respond to SHBG+T better than they do to pure free T. Why? SHBG is brought into a cell via the extracellular megalin receptor, where it is used to prolong the activity of steroid molecules within a cell. Without SHBG, free testosterone is rapidly glucuronidated and effluxed from the cell. SHBG and T work in concert.
The literature provides us with a case of a totally SHBG deficient male. His complaints were low libido and low musculature, even though he was otherwise fully androgenized. These complaints were not remedied with testosterone supplementation. The study authors concluded that a tissue dependent effect of SHBG on androgenic signalling was proven. The doctors treating the 0-SHBG patient gave up on testosterone replacement and decided to pursue methods of increasing his overall energy level.
It appears, thus, that SHBG is required in sufficient amounts in tissues like muscle that require a very high level of androgen signalling.
Moreover, there is an extracellular receptor for SHBG that requires SHBG to be unoccupied by a hormone to bind. Once bound, it catches a free steroid molecule and completes the extracellular AR signalling pathway. If SHBG is low, this activity can be nearly completely inhibited.
One interesting thing to note is that on a protien-per-molecule level, SHBG and testosterone are produced in nearly identical quantities. The molecular weights of testosterone versus SHBG are very different, but by serum concentration, a healthy male produces slightly more SHBG than he does testosterone. This is actually required for proper hormone balance and function.
There are no studies that show an independent effect of free testosterone elevation on musculature. This is pure conjecture based on ill-informed "broscience" mythology. In all studies where testosterone positively correlates with lean tissue growth, total testosterone is increased proportionately to SHBG and FT% is within the normal range.
If we look for a case of testosterone administration with low SHBG and a therefore excessively free testosterone percentage, and expect to see better "results in the gym" -- we will not. We have not.