If I want to drive from California to, say, South Carolina, what is a fast yet scenic route?

Things I would like to see: flower fields (I love those huge expansive fields of flowers you see in calendars), lakes, national monuments, strange/interesting "only in America" places.

Probably Interstate 40 to North Carolina and then depending upon where in the state, you can drive down.

Fast and scenic don't go together. If you take the Interstate you have a hard time pulling over and enjoying if you see something you like. Not the fastest but you could take US-80 part of the way as time permits. In the good old days it ran from LA to Savannah.

RedRock is absolutely correct. You can't have your scenery and bypass it too. Your request simply isn't reasonable. Not to be critical, but if your objective is to go fast, then go fast. The suggested route is probably the best, even if you really just want to "make good time" but plan to stop at interesting places that might pop up along the way,

OR, you could spend a few days exploring one area.
Then, marathon all night drive it the rest of the way.
I personally would jump off route 40 and spend a few days in the ARizona/New Mexico area seeing the Grand Canyon, Sedona Monument Valley, Petrified Forest,
Then I would do a marathon drive across the rest of the country with no stops.

Depends on the time of year, especially if you're looking for flowers. When are you doing this, and how much time do you have?