Of course, celastics are not skived, but you can adjust the stiffness (due to control of the acetone) within a celastic toe-puff: rigid at the tip and quite floppy at the end. The skiving not only reduces thickness, but also adjust the stiffness within the piece. I haven't got a toe puff on hand, but in a hand-skived counter, the thickness varies from about 2.5 mm to virtually nothing at the edges. The thickness of the celastic is the same all over: it is the thickness of the actual cotton weave.
I am not talking about celastics in handmade shoes but in factory work. Rendenbach used to produce counters and maybe toe puffs as well, pre-cut, pre-skived and pre-shaped (they might have stopped production, as I cannot find them on the website any more). I never said a celastic was preferable to a carefully hand-skived toe puff which, once in situ, is then rasped into shape (and possibly get an additional strip of torn newspaper glued over).
I don't know what "needle toe boots" are - are they those ridiculously pointed cowboy boots? Maybe 50 years ago, when Teddy-boys wore "winkle pickers", English shoe may have had heat formed plastic stiffeners as well. The Northampton factories might still have the heat moulding machinery in the back, but as far as I know, everyone uses celastics (at least for the toe).