GKU- we did many miles per day when we went but we had some friends that went with us that only had a week of vacation.
We have family in California and we have also drove the way you mention. I think the way you have might be shorter distance but you end up going through more city driving instead of interstate speed. Also, depending when you are going, that route will take you in higher elevations and might have weather concerns.
If you have not driven through west Texas on I10, there isn't much out there.