If you only play one game (that would take about 15 minutes to play) then yes, the person that draws The Crown is likely to win, I've only seen a handful of games where the person that draws it has less points than someone else. Played this way the game is good filler, which works pretty well actually. Drawing The Crown is critical to winning.
Also, We have added 2 Variant Crowns, one at 5 points and one at 8 points. So if you'd prefer to play without that mad dash for the Crown, you can play with a Crown that is worth less points.
But, JunKing is designed to have multiple small games as 'rounds'. So in the same way you would play rounds of Hearts, building up points from game to game until someone hits a point total, you would play JunKing. Or you can play rounds equal to the number of players as well. Then the game becomes a long term strategic game instead of a mad dash.
Also note that the Perfectly Good Sandwich card that is shown in the Game Contents section is one of 3 such cards in the deck, and that can give a huge boost to help overtake the person that drew The Crown. (And you can hold 2 such cards since they are devices).