The scale of the resorts in the European Alps compared those in the Rockies is quite different. To take an example, consider
St. Anton and
Alta as described on Wikipedia (excerpts below). The skiable area around St. Anton is listed as 167 sq. km. (64 sq miles, 40,500 acres), while Alta is 10 sq. km. (4 sq miles, 2600 acres). Snowbird on the other side of Mt. Baldy is about the same size as Alta. But Alta/Snowbird combined is still far smaller than St. Anton. The vertical at Alta is about 2500 ft, compared to close to 5000 ft for St. Anton. Alta has 4 chairlifts and a transfer rope two between the two bases.
Alta terrain is described as 15% green (easiest), 30% blue (intermediate), 55% black (most difficult). Alta Ski Patrol is actively managing 100% of that black terrain. Often the most challenging areas are closed for a few days after a snowstorm, which can include groomers below areas that are avalanche prone. My impression is that's not how it works at European ski resorts.
My home hill (near Washington DC) is much smaller than ski resorts in the Rockies. There is no off-piste terrain at all. The open trails are fully dependent on 100% snowmaking. A long run at my home hill takes 3 min to finish for an advanced skier, 5 min for an intermediate. It's sometimes hard to explain how that can be fun to folks who have only skied at big mountains in Utah, Colorado, or California.
St. Anton in Austria
"St. Anton is part of the Arlberg area of ski resorts – a region that includes 94 cable cars and ski lifts, 340 km (210 mi) of groomed pistes and 200 km (120 mi) of deep-snow runs, all of which are covered under one liftpass.
. . .
The groomed runs in the region cater to all levels; 43% are for beginners (blue), 41% for intermediate skiers (red) and 16% are for the more advanced (black). There are also 200 km (120 mi) of deep snow runs in the area.
Expert terrain includes less-frequently groomed ski routes such as Schindlerkar and Mattun, and the backside of Valluga (2,811 metres or 9,222 feet) down to Zürs, which is for experts only if accompanied by a guide. There are also a large number of off-piste routes in the area that experts can explore with the help of a guide."
Alta in Utah, USA
"Alta is a ski area in the western United States, located in the town of Alta in the Wasatch Mountains of Utah, in Salt Lake County. With a skiable area of 2,614 acres (10.58 km2), Alta's base elevation is 8,530 ft (2,600 m) and rises to 11,068 ft (3,374 m) for a vertical gain of 2,538 ft (774 m). One of the oldest ski resorts in the country, it opened its first lift in early 1939.[2] Alta is known for receiving more snow than most Utah resorts,[3] with an average annual snowfall of 545 inches (13.8 m)."