The no week long trips isn't about boredom, it is just that this is the first true ski vacation or vacation with skiing that we have ever taken. We are a ski race family, so we are generally at our home mountain training, or on the road for the duration of the races. We have never had a chance to take a vacation like this. It just didn't even register with us that staying put was more common the bouncing in and bouncing out.
There are plenty of smaller resorts that people bounce between for shorter visits, but the whole point of the really big areas is to have the variety of multiple resorts without having to relocate. Bouncing between them is like bouncing between Summit Co and SLC.
It’s certainly possible, but as an American who’s lived in Europe for a while, I think you’d have a more enjoyable time if you picked two areas and skied each for a week, because that would give you more time to explore and take advantage of the different type of skiing you get in the Alps. Also, in case it snows while you’re there, you’ll still have days left over to explore, and you won’t feel like you didn’t get to see an area.
FYI, this is what skiing in the Alps can be like when it snows (not my video). This is one of the blues in Tignes.
I’ve had December trips to Val d’Isere and January trips to Verbier and St. Anton in recent years where it was like that for four or five days in a row.