Best way to travel from Vegas to San Francisco?

My husband and I (both 33) are planning to visit the States from the UK in October.

We're looking at flying in to LA and out from San Fran for 11 nights.

Days 1-4 - travel from UK and LA sightseeing

Day 5-7 - Vegas via public transport

Day 8-10 - rent a car, drive to the Grand Canyon and then to San Fran via the PCH

Day 11-12 - San Fran and flight home.

With our airmiles there isn't an option to start in Vegas, so need to start in LA.

My question is, is the PCH worth doing, or should we drive straight to San Francisco via the quickest route?

Should we scrap Vegas from our plan and spend more time on the PCH rather than a couple of days? Or instead of driving to the Grand Canyon, book onto a day trip from Vegas?

TIA 😊