Like 1's easy to clinch thread, list roads that have things like seasonal or governmental restrictions, or just even poor to nonexistent signage, that make it difficult to clinch a road.
I'll start with WA 20 - seasonal closure over the Cascades
Nexus 6P
I started to write this as a contrary example in the "by accident" thread.
I will confine my comments to routes of 500 km or less. In California, for instance, clinching CASR-1 or US-101 requires a lot of effort both due to their length and the illogic of traversing the entire route.
There are a lot of routes in California whose individual segments make sense and the adjoining ones all make perfect sense, but which traversing the entire length is either illogical or difficult due to discontinuities.
The prime offender is CASR-65. It was intended to be a 500 km long route to parallel CASR-99. What exists today is 2 100 km long segments separated by a 300 km route that is currently undefined and unconstructed.
I believe that it is CASR-178 that poses similar problems (but the unconstructed portion is short and really inconvenient to get from one part to the other).
CASR-41's segments make plenty of individual sense, but no one really goes from Morro Bay to Yosemite. Fresno to Morro Bay? Abosolutely! Fresno to Yosemite? Of course.
CASR-16 is discontinuous and illogical as an end-to-end route. You'd have to make a concerted effort to clinch it.
CASR-4, CASR-84, and CASR-160 are perfectly logical in segments, but don't make as much sense as end-to-end routes.
I could say the same thing about CASR-12 and CASR-33.
A lot of California's East-West state highways (like CASR-41) tend to have a logical center point and logical end points but no obvious reason to go between the two end points. CASR-180, -198, -152, -156, -299, -20, -46 all fit the bill.
... and all of that without introducing any technicallities such as the easternmost 3 meters of the route's being blocked off by a gate or a bridge that has been out for 15 years or that the westernmost 100 meters requiring a ferry that only operates two months of the year or the like.