When is signal strength ever an issue, unless you've got a broken pickup? Sure, you need to adjust the volume of your amp, but that's about it.
It may be an issue if you don't want the amp's input driven so hard that it creates overdriven distortion type of tone and you don't want that affect and want to preserve your "vintage" output and character (like installing some Texas/Hot pups for example). I prefer to leave the guitar's vol control full up most of the time for best tone since rolling it back loses high end which I don't like and I'm not a fan of treble bleed caps in situations where it causes the pups to become too bright and tinny or thin sounding.
I'm also just not that fond of the upper half of the TBX controls.
It has it's place for certain amps & songs. And yes, it "sinks tone" or bleeds off high end from the center detent downward. But from center upward it is described to increase highs and presence. And I've also heard people describe it as increasing treble from the center up while lessening the bass. So it is a sort of Treble AND Bass control then by definition.
My point is that it's also variable in it's adjustment to get just a tad more of one or the other too to "dial in" just the right amount that's needed.
So as HBP was describing - real '59 humbuckers being lower output and brighter - (I love this in a HB pup and why I have a Seymour Ducan SH-2n Jazz in a LP) is a better tone to which brings out more character and clarity from the instrument. I also have this pup wired for series or parallel because the parallel brings this out even further - a great tone to me since LPs can be so dark all of the time.
So since most humbuckers can be darker sounding (w/ plenty of bass too) - having a TBX tone control for one of these might be of more benefit to this kind of pickup allowing the bass to become lowered or rolled off while increasing the highs & presence at the same time - like having an on-board EQ control rather than the generic "treble sink" as you put it. This type of tone control (TBX-type) is never associated to be used in Les Paul-type of guitar that I know of. I'm very intrigued by the use of this combination together. Has anyone ever actually tried this? And if so, what was the outcome?
I can see that the no-load control would be the better option for a single coil rather a TBX because those are already bright & trebley w/ presence. Now, since 60Hz hum has been anoying me while playing out I've bought some Lindy Fralin Split Blades for one of my Strats. These are supposed to be clear and bright like a single coil w/out the hum of course. Maybe a no-load would be the right choice for these too? But some other lesser "humbucking single coil" pups may "need" the TBX control to insert those highs & presence back as much as possible since these are - for all intents - humbucking pups afterall.
HBP - your description of a TBX control being a "mid-boost" is incorrect. The EC strat has an "active mid-boost circuit" in it to do just that effect which is what you're thinking about. The TBX tone control may actually be just the ticket to get that original '59 tone quality out of normal humbuckers?!?