The long-lasting nature of those photographs isn't so much due to the glass plates as such, but the choice of glass plates over the film of the day. The nitrate (nitrocellulose) films of the era degraded quickly, became brittle, and had the quite annoying tendency of bursting into flames. (They're made from a close relative of gun cotton.) The gelatin emulsion is still delicate and prone to damage from things that eat it (fungi and insects, mostly. Glass plates are (obviously) fragile, and are probably more of a problem than current sheet film (which is acetate- or polyester-based; acetate films can degrade if not stored properly, but polyester is nearly indestructible).

But certainly you can make and use plates. (You can even buy them, but they're mostly for astronomical use.) You can purchase traditional emulsions, like Rockland's Liquid Light commercially, which will develop with standard black-and-white paper processes (most are orthochromatic and designed for printing rather than for negative/plate; panchromatic emulsions for negatives are much harder to find, and usually come from garage-sized operations, but they'll develop with standard film developers and processes). And please note that "Diazo" emulsions are not what you want; they're UV-hardening emulsions for the screen printing (serigraphy) process. But the current vogue process for DIY plates is wet collodion.

Either way, you're going to wind up with a negative/plate that shows inconsistencies and flaws, simply because you won't have the carefully-controlled conditions and equipment needed to apply the emulsion in a uniform and completely predictable manner. If you accept those inconsistencies and learn to create them in a semi-controlled manner, you can achieve some very pleasing effects. (That's particularly true if you use a Petzval-design lens wide open.)

That said, sheet film isn't all that hard to get. It is expensive, but then it always was. And it was never (at least not in my lifetime) something you could find at the corner store; you needed to depend on large photo stores. B&H carries a good selection, as does Calumet Photo (one of the last remaining hard-core large format/view camera shops in North America). I'm sure you could find others just about anywhere in the world if you looked.