Not shamefully, but you have misinterpreted the general idea. You assume that total testosterone doesn't change. But if underlying metabolism stays the same then free testosterone must be preserved to maintain the consumption/excretion rate. So it is total testosterone that adjusts to make it work." As noted, the rate of use and excretion of testosterone is proportional to free testosterone."
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Have I shamefully misinterpreted your statements?
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Call it an informed hypothesis supported by anecdotal evidence. The primary assumption that might be questioned is that underlying metabolism, e.g. in the liver, does not change. I've observed mine to be static over several years and at various SHBG levels. I expect this is not unusual, but there are certainly going to be exceptions....
"Suppose your SHBG suddenly changed dramatically. What happens at the new steady state? You must still be excreting the same amount of testosterone each week. Thus free testosterone must be unchanged after the transition, and total testosterone adjusts to preserve this level of free T at the new SHBG."
Is this a hypothesis or something that has been proven? This sounds highly theoretical.
The point about testosterone intake matching use/excretion is straightforward. It assume no endogenous production. Therefore at steady state the average rate of testosterone being injected is matched by the average rate of testosterone being used/excreted. This is important, because with the rate of use/excretion proportional to free testosterone then average free testosterone is proportional to average dose. And here are some of my actual free testosterone values versus dose:
These points had to be acquired with frequent injections of longer esters—enanthate, cypionate—to avoid half-life effects.
In any case, taken together these arguments support the premise that in those on TRT injections, a sudden change in only SHBG would result in an adjustment to total testosterone, not free.
If you'd like to visualize what's happening with an analogy, I describe one involving tubs of water here.