Except "modern" paper is utter crap and won't survive past a few decades, contrary to some very old paper that is still almost intact centuries later.
And of course, the minimum for the printing itself would be to use a laser printer, but even toner is not going to last longer than a few decades (depending on storage conditions). Maybe that's enough, but that can't be compared with some ancient paper sheets and inks that were made with completely different (and more durable) materials.
I think you are somewhat misinformed.
Certainly there is no evidence that “modern” (in the sense of what we can buy now) office papers only last a few decades, and we have papers from every era survive perfectly fine. In fact, papers from the early 20th century age
worse than more recent papers, since we learned from the problems with early-20th-century papers.
In the 1980s, all halfway-decent papers were switched to acid-free formulas/processes, eliminating the source of most deterioration: acidity. (And in fact, there are bulk processes to deacidify paper that isn’t acid-free. Archivists use those methods to stabilize entire archives of documents printed on pre-1980s office paper.)
The papers that survive really poorly are the extremely cheap papers used for newspapers and inexpensive paperback novels; those start to yellow after just a few years in suboptimal conditions. But nobody would
ever select those as an archival medium! You’d use a quality archival paper.
And it’s not as though
all old/ancient papers and inks survive well. Archivists and historians have to deal with deteriorating documents all the time. Many of the inks used in antiquity are really awful, and either fade or damage the paper, or both. The common iron gall ink that was the dominant ink used for over 1400 years in the West is acidic, and sometimes eats through the paper. (Modern iron gall ink is formulated differently so that the acid evaporates quickly, reducing the problems. It’s a niche product now, though.)
As for what printing method to use: toner is good if the paper is kept cool and above all
not in contact with soft PVC, whose plasticizers leach out, causing the toner to adhere to the PVC and release from the paper. In particular, monochrome laser is excellent. But honestly, if I were choosing a printing method, I would probably use inkjet. Modern pigment-based inks are very stable, and are waterproof. Since they absorb into the surface of the paper a bit, they can’t easily delaminate. (But one must choose an inkjet with ISO archival compliance, not just any old whatever from Best Buy.) I could also imagine that someone could make (if there isn’t already!) inkjets with specialty inks that adhere extra well and perhaps are also solvent-resistant.
Archival inks are a known technology. (Germany, for example, has specific standards for archival inks in pens, and requires many types of important documents to be signed with pens that have archival inks. There are similar standards for printer inks and toners.)
There are gazillions of toner-based photocopies from the 60s and 70s that survive just fine. Even those stored in mediocre conditions are usually okay. (Other than the aforementioned contact with PVC.) Heat and pressure can cause toner to slowly release to adjacent sheets, especially if the fusing process wasn’t ideal when the print was made. Stored dry, cool, and dark, toner survives well.
So if you’re talking about archiving historical documents and items originally intended for everyday use, then conservation of materials with poor archival characteristics is a big problem. But the context of this thread is
deliberate archiving, with careful selection of materials for that purpose. There is no reason to doubt the longevity of these.