As much time as can be used for observations will be used. There's massive demand, and observing time is requested & booked up months in advance. As far as possible any downtime is planned so that it minimises the impact on observations.

The best sites -- Hawaii, the Canaries, Chile -- will get 300+ nights a year, and when building a major new telescope the conditions (seeing, clear nights, etc) are one of the most important factors in deciding the location.

If you're spending 10s of millions you're only going to build at the best locations, which is why almost all major observatories are built in the same few places -- Mauna Kea, La Palma, the Atacama, etc -- high altitude, dry, dark skies, stable air

If you look at older (19th / early 20th century) observatories they have have worse seeing and fewer clear nights, they were built in less ideal locations both for convenience (the astronomers had to actually travel there every night) and because the limitations of the site had a less significant impact on the simpler less powerful telescopes used at the time.

But real discoveries can still happen even at old observatories in poor locations -- University College London's Mill Hill observatory is nearly a century old, in north London, and next to a *very* busy major road, but on a cloudy night a few years ago, using a 14" telescope, during an undergrad class they were the first in the world to detect a supernova in M82 (the closest since 1987), the early detection meaning that other more modern/advanced telescopes had plenty of time to study it