I'm all for simplicity, and, again, this isn't an argument against Dart. But I would still contend that merely shrinking your DOM API surface area is only of marginal significance.
Historically, the hardest part of interacting with the DOM has been the inconsistencies (and missing functionality) amongst ancient browser versions. We've had standardized methods for a long time now that make DOM interactions relatively trivial if you have the luxury of working with browsers that support them.