It seems you rely on reading music a lot more than I do so I can't really put myself in your shoes...but I'll give it a try.
Well there's the answer right there!
If you're not relying on reading the music as you play then you're basically playing by ear, memory, or improvisation.
Typically you don't really need to even think about what actual notes you are playing when you do that. Once you've learned scales and basic fingering you just go with that.
I do that sort of thing all the time. For example, if the band is playing in the key of G, and I'm playing an alto sax, then I know that I need to play in the key of E. So I basically start to think of E as being G in that sense. I don't even think of individual notes, I just think in terms of the key I'm currently playing in. I don't even really need to name it. It's just a fingering pattern for a scale is all.
The reason for transposing instruments is definitely associate with actually reading music real-time-live like in an orchestra or a formal band where the players are actually reading from music that is on a stand right in front of them.
If you aren't relying on reading music, then of course none of this is going to make any sense to you. You don't need to be bothered with any of that. You're either playing by ear, or from memory.
I asked you before to explain what you meant by "de-transposing" your instruments. You simply replied that you always "think" in terms of C. But what does that mean?
Does that mean that I can hand you sheet music written in C and you can just play it straight-away on your saxes by reading the music written in C? If you can't do that, then you haven't "de-transposed" anything. All you've done is learn to play by ear and think in terms of C.
Like I say, for improv that's typically the way it's done anyway. Once a person knows what "key" to play in, they don't even need to think in terms of notes names or keys beyond that. All they are doing at that point is thinking of fingering patterns.
So all you're telling me is that you do the same thing I do. When a band is playing in G you just pick up your Alto sax and play in the key of E and think of that as being the key of G.
I do that all the time for all the keys. Just tell me what key the band is playing in, and I'll find that key on the alto sax real quick. That kind of "transposition" is a snap. And once I know what key I need to play in, I no longer need to think of keys or note names, because from that point forward I'm just playing by ear or by improv anyway. I'm just playing a fingered scale pattern at that point. I don't even need to give it a name at all at that point.
That kind of "transposition" is simple once you've learn the circle of fifths. That's they key right there. For the Alto sax it's extremely easy. Whatever key the band is playing in all you need to do is play in the relative minor key. Of course you play a major key, but the transposition is a snap.
And, like I say, if you are playing by ear or by improv, once you've recognized what key you need to play in it's all just finger patterns from there on out. You no longer need to think in terms of keys or even note names for that matter.
So unless you can play your saxes directly from reading sheet music written in C, then you haven't "de-transposed" anything.