The Skins would be major players, but I don't think it's really a "dream situation." A "dream situation" would be like MLB where teams like the Mets, Yankees, and Boston are the only teams in an elite level of money that the other teams can't compete with on a year to year basis.
In the NFL, there's probably 9 other teams that can compete with the Skins when it comes to money. While the Skins are the most valuable NFL franchise currently (which is likely to change if/when Dallas gets the new stadium), there are about 9 other teams that have the combination of generating enough team revenue along with having far richer owners than Snyder to compete.
The Seahawks are a perfect example as they are about $300 million less in value than Washington, but Paul Allen is a far, far richer man than Snyder.
In the long run of an uncapped league, the big market teams would be akin to say the Atlanta Braves in that they would have one of the top payrolls and chances are they would consistently have solid records, but it would still take some good coaching, scouting, and decision making to ensure that would happen.
Rich........