A few years back, I have noticed by accident (I forgot to press the octave key while practising one of the musical pieces) that I can play all the notes on the tenor saxophone that normally require the octave key to be pressed without even touching it. I have never deliberately practised harmonics, and I have not attempted altissimo yet.
Recently, I have asked my teacher whether it is alright to play without using the octave key, and he said that he knows plenty of saxophonists who don't touch it "because it's just another key that needs to be pressed", but he thinks that the notes sound off by about 10-20 cents when played without the octave key and don't have the same "feel" to them (and that's true for his MKVI), so he recommends using the octave key. I've spent some time with my tuner and found that for my horn this is not the case. The notes sound absolutely the same (I've even recorded them, to make sure that it's not an audial illusion), whether I utilise the octave key or not. In fact, it is much easier for me to play notes that require palm keys that way (including F# which, with the octave key pressed, I cannot even get out of the instrument, unless I approach it from below, like E). I have not tested it with fork fingerings yet. At this stage, I don't even know anymore whether the octave key does anything at all, or if the sound comes entirely "from me".
My question is the following (and I am happy to remove it if it's an opinion-based question): should I start playing without the octave key if it works so well for me, or am I potentially setting myself up for some problems down the track, like with altissimo? Because this technique allows me to do huge jumps (12 or more semitones) seamlessly, some of which even my teacher has never been able to perform.
I am also curious as to how the overtones are produced, because I have never practised them, and they just came to me naturally. I have tried to notice if anything changes about my embouchure or throat when I play them but couldn't really find out how I do it.