I’ve driven the whole thing maybe 10 times, with some trips running only on selected portions. It’s fun. It’s also slow. Driving it now makes you realize it must have been hell when all the traffic that currently runs I55/44/40 was on the route. There are places I hate to meet cars now - blind corners, narrow bridges, etc.
There is a lot still extant. Nearly all of the last route exists in Illinois, Missouri and Oklahoma. It just isn’t called 66, but it’s the same road. A lot exists in Texas and Arizona, but most of that is short runs, and you have to get on the freeway for long stretches. There’s not much to see there, anyway, so it doesn’t matter. The view of empty desert from I40 is exactly the view you would have gotten on Rte 66.
Some of the areas I’d hate to recommission are the former four lane alignments in Oklahoma. The route is fun now, as you can see the old extra two lanes there, and wonder at what it used to be. But should they be recommissioned, too? A lot of bridges are old, and decaying, and unsafe, and closing. What do you do about them? There used to be these two twin bridges just north of Catoosa, OK, but one of them needed to be replaced. Now there is one old classic bridge and one new boring (but safe!) bridge. Is that still “66”?
Another area is the single lane (center) paved section south of Miami, OK. The road was paved only down the middle to save money. But it is still the original pavement, and it is decaying. If I lived on it, I’d want it paved. But as a tourist, I love it. But it has decayed noticeably even in the 15 years I’ve been following the route. What do you do about that?
What they should have done is called I55/44/40 “I66”, because that’s what it really is. As noted, the alignment has changed several times over the decades. It had been updated to accommodate the increased traffic over the years, and straightened and fixed up for safety. The interstate really is the logical successor. The route would still have been continuous, and updated for modern traffic. It would have been the “legitimate” 66, just like Washington’s axe. 
I would think the best thing overall would be to renumber the route as “state 66” in each state. Because many of the surviving sections are state highways now. Just change the number to 66 and leave it at that. Would make it a lot easier to follow!