The fabric can still be found- even today there are some decent gabardines, and heavier serges, twill, and tweeds.
It's also the materials within the suit- woven canvases, animal hair, etc etc vs modern synthetics.
Plus, a lot of things today are fusible, glued, or tacked with nylon thread.
I'm kinda babbling here, but in essence, most tailors today will prefer to use MODERN techniques and supplies to imitate the LOOK and DESIGN of a vintage suit. The great hurdle is getting one to go "old school" and spend a lot more time, NOT using modern shortcuts and conveniences.
Most of the reproductions I've seen look nice, but to the trained eye, they still look modern. I know Jorge (La Bomba Vintage) has done some great stuff.
IMHO, Magnoli Clothiers looks... eh. Even their photo examples, which should be your "Best of the best" look loose, frumpy, and unshaped.
I've considered ordering some of the Wool Elastique fabric for Officer's "Pinks" but the aforementioned review makes me skeptical....