The break what would be for players of non-playoff teams would make it too difficult. Nowadays they have basically 2½ weeks between the end of regular season and the start of WHC which can allow to take a week easily, then go to the camp and then it's tournament.
European teams mostly start their camps without top 4 teams of each league and it takes few weeks so there are not that big breaks.
Just thinking, I took a look on Canadian, US and Swedish World Cup teams. Here's how they stand regarding when their club season ended or who are still in the hunt. Pretty much showing that dream teams have lots of players from worse teams.
RS: Doughty, Muzzin, Duchene, Giroux, O'Reilly, Stamkos, Tavares
Round 1: Crawford, Price, Burns, Vlasic, Weber, Bergeron, Couture, Marchand, Thornton, Toews
Round 2: Holtby, Bouwmeester, Pietrangelo
Still playing: Crosby, Getzlaf, Perry
RS: Bishop, Quick, Schneider, Byfuglien, E.Johnson, Abdelkader, Palmieri, Wheeler
Round 1: Suter, Backes, Dubinsky, Kane, Pacioretty, Parise, Pavelski, van Riemsdyk
Round 2: Carlson, McDonagh, Niskanen, Oshie, Stepan
Still playing: Kesler
RS: Markström, Ekman-Larsson, Hedman, Strålman, Eriksson, Landeskog, D.Sedin, H.Sedin, Söderberg
Round 1: Hjalmarsson, Backlund, Krüger
Round 2: Lundqvist, Berglund, Bäckström
Still playing: Enroth*, Ekholm, Karlsson, Lindholm, Forsberg, Hagelin, Hörnqvist, Silfverberg
* Ducks property, but not in the playing roster just now.