Part of the problem is the geographic maldistribution of federal land holdings. In the east, beginning in the early federal period, federal lands were rapidly privatized to accommodate homesteaders. As settlement moved into the semi-arid western plains, it was found that larger and larger acreages were needed to support each farmer/rancher. By the time we reached the desert and mountain west, the land really wasn't suited to agriculture and the primary value was logging and mining. Congress eventually (the 1880's?) changed the law, and the feds kept title to most of the land. We are left with massive federal landholdings in the west and tiny bits and pieces in the east. Fast forward to the 21st century, and this is a very poor solution for national park needs.
The obvious solution is to privatize federal lands in the west and use the proceeds to expand park holdings in the east. (I'd also use proceeds from the closure of military bases for the same purposes, instead of just giving these often very valuable properties to local governments.) IMHO, this would be a good strategy for the park system. It would also help with the politics of land preservation by reducing the resentment factor in the west, where the feds too often are an abusive landlord, and by increasing park accessibility in the crowded east, where it is needed.
Last but not least, I would place an emphasis on urban and near-urban parks, and try to make these big enough to be a real respite from urban sprawl and suitable for mixed use. Historic sites and waterfronts are obvious places to begin. The total federal acreage doesn't need to increase if it were appropriately redistributed. This isn't something that can be done overnight, but if one drew appropriate boundaries for future parks, one could set about the long process of land accumulation as properties came onto the market.
Federal management of National Parks has been little short of disastrous. Why would you want it?
Privatize all of it. You'd see a "park industry" in short order and it would be better maintained because they would have to compete for customers. There is really no need for a socialized land entertainment and wildlife management entreprise.