Because DLR tends to have more short-term visitors than WDW, there isn't as big of an emphasis on table-service restaurants. Instead, there's a great variety of mid-level "buffeteria" locations that serve pretty good food in a faster format. These locations all feature "real" plates (heavy-duty plastic) and actual metal silverware. These not-entirely-flattering photos were posted in various online reviews; they're clearly not staged photos from Disney
Plaza Inn in DL
Cocina Cucamonga in DCA
The standard quick-service locations tend to serve their food in plastic baskets, lined with wax paper. Still very casual, but somehow it feels fancier than simply eating off paper plates. These locations have plastic silverware, but tend to serve finger food
Hungry Bear in DL:
Award Wieners in DCA:
For comparison, WDW's only real mid-level option, Sunshine Seasons at Epcot:
Additionally, since WDW guests tend to visit longer, they're much more likely to get tired of eating off paper plates for a week, rather than guests who visit for a day or two. And given how much Disney tries to push the "environmentality" brand, you really have to wonder how much waste is created by all those "disposable" food service items for the roughly 140,000 guests in WDW's parks each day, presumably eating multiple meals