My wife and I visited this region and had a chance to drive these freeways last week. Several comments.
The Ok Connector is an outstanding road that rivals anything in the US Interstate system! It is unfortunate that it is unfinished to its original planned connection to the Coquihalla about 30 km south of Merritt, BC. As a compromise, BC widened the Princeton/Kamloops road to 4 lanes into Merritt. While this brings people to Merritt, it lengthens the trip from points west to Kelowna, BC. It has been stated that the Merritt populace objected to the original plans because it would have many people bypassing their town on the way to the Okanagan. Have they not heard of Outlet Malls? Build them and they will come. Meanwhile, I would encourage the BC Trans ministry to eventually complete this road as originally designed.
The Coquihalla Highway is decent freeway, also. The rugged geography south of Merritt does command some steep (8%) grades and curves that made us slow down, at times. It is evident that this portion of highway is susceptible to avalanches in a great many places near the Coquihalla Summit. The freeway north of Merritt is well engineered to "interstate highway standards" to Kamloops.
Because through traffic from Vancouver to Kamloops and on to Calgary is most likely to travel this road, I would propose this be designated the Trans-Canada route. Highway numbers remain the same but TC-1 through the Fraser Canyon becomes BC-1 and the Coquihalla becomes TC/Yellowhead 5.