EUV became popular around 1996 as part of the NGL frenzy. People sort of realized there was no good lithography wavelength after 193 nm. Intel was quite familiar with the known choices (like hard X-ray, e-beam, etc.), but knew far less about the extreme ultraviolet range below 100 nm. Those days, people only expected NA to go to 1 (immersion not yet considered) and k1 was not yet considered a knob to be tricked with yet, so wavelength was considered the only scaling knob.
The trouble was a wavelength still had to be selected. It was a drastic leap into the unknown. 13.4-13.5 nm was chosen for most convenient optics available at the time (Mo/Si multilayers). Other properties not known. Unfortunately, today we know that it's hard to get a lot of EUV power, and resists don't respond ideally either. Defects can be buried in the multilayers. The industry is supposed to have learned its lesson.
It doesn't make sense to develop a new wavelength over several nodes and then use it over half as many. Moreover, EUV light source consumable is a big waste of tin. Studying the resolution with electrons would have made more sense.
EUV represented a knowledge gap which all the companies funded to fill. Optimists always bet on the newest unknown, and the probabiliy is always going to be 50/50 at first. However, as requirements tighten over the years, the odds are not in the favor of the original rosy expectations. Now that EUV's nature has been made more clear, it doesn't look any better than X-ray or e-beam.
The more things change, the more things stay the same. X-ray was supposed to replace optical in 1985. It is supposed to replace optical now in 2015, under its new pseudonym, EUV. E-beam direct write was going to replace masks in 1985, at the very least, for low volume. It still is, under its new pseudonym, multi-beam maskless. Perhaps if 8-track stereo, VHS, and DEC changed their names, they'd still be around too. The only new and novel technology is nanoimprint, which is more optical than any of its challengers: it uses an I-line source, I-line resist, and 6"X0.25" optical photomasks. It also happens to have the lowest cost of ownership of any of them, including, easily, double patterning. The only thing it hasn't yet done is change its name: it remains nanoimprint and its a lot better bet than either of its re-named competitors.
P.S. EUV is still X-ray, and multibeam maskless is still e-beam direct write. Mother Nature is funny that way.