If you're traveling to another continent for a vacation, you're probably not that budget constrained.
Also,
four weeks is a very long vacation, so you don't seem that time constrained either.
Not trying to call you out or insult you, just saying what you're doing is wayyy more than what a lot of people could ever hope to do, especially because you're only 18.
~ @Enron
Though @J055Y_ must not be the most constrained, I think the point is to skip over most of the middle of the US. Not to insult the middle states but there aren't as many iconic images there (sorry @OneBreadSlice ). The options were to fly straight to the West and look around there, fly to the East and stay there, or pay to fly a SECOND time to visit a bit of both. The trip is spaced out to give large amounts of time at the large cities and National Parks while quickly checking out some other side areas. If more than a couple more places were added the trip would be spent driving almost the entire time (something @J055Y_ 's family may not be so used to). It's planned out to give time to see a fair portion of many of the areas.
If you look over the general travel times you'll notice a pattern. After the visit to New York and the flight to Denver, the trip moves down south. It's 4 hours to Del Norte and after a plane trip, it's probably where they're staying a night. As far as I can tell, it's not filled with interesting places.
Taos and Santa Fe might be on the same day since combined it would be less than 4 hours. El Rancho, New Mexico doesn't appear the most exciting place either so it's probably somewhere to rest before moving up north to see the sandstone deserts of northern Arizona and southern Utah. Monument Valley should be nice and the Grand Canyon will probably be a quick stop up on the way to Bryce. There's probably a stop near Monument Valley (I'm assuming the Arizona side since it would be weird to cross into Utah to then return to the border with Arizona to see the Grand Canyon).
Bryce makes the most sense out of southern Utah parks because it's got the most original structures. The lack of visits to Arches park does appear to back up my intuition that most of the time here is spent quickly with only a couple days for each of the Colorado, New Mexico, and Arizona/Utah sections.
Las Vegas is misnumbered in the list, possibly since most of its allures are more casino based so the trip could just have a quick drive through the area (just like with the Grand Canyon). Apple Valley is a smaller city so I assume just like with Del Norte and El Rancho that it acts as a stop for the night on the way to the California coast. It works best to rest near Bryce and pass through Las Vegas (a six hour drive) instead of visiting Bryce then stopping in Las Vegas since a rest at Monument Valley would make the trip to Las Vegas about 8 hours (longer than any other drive), but if there's a rest somewhere in Utah before visiting Bryce it's still possible to stop at Las Vegas after a drive of 6 hours or less.
Each of the destinations are 2-6 hours apart making it most likely for @J055Y_ to follow directly up to Mammoth Lakes, rest, go through Yosemite National Park to do sight seeing, and rest again before going down to San Francisco.
As far as I can tell, the trip is spaced out to be pretty quick between destinations giving the first four states after New York about 6-8 days, Nevada a day, and California before San Francisco about 4-6 days. That gives time to be largely distributed between the two large cities of San Francisco and New York of almost two weeks. Perhaps a week at New York, half at San Francisco, and some extra time to check out Bryce, Mammoth Lakes, and Yosemite?
I'd say this schedule is decently well planned out. Of course plans also depend on how much driving at a time the group wants to go. If you're like my family, you've taken a trip or two with 10-15 hour drive times for multiple days, but some groups may only want to drive up to 3 or 4 hours at a time.
