Adding a route to a road network does not itself reduce total capacity, of course. It's actually a queueing theory issue--misusing a road as a dysfunctional queue by putting more cars on it than can get through causes head-of-line blocking and allows cars taking the congested, shorter route to obstruct the clear, longer route. (this is concealed in the Wikipedia article by describing the travel time as Travellers/100, the latency of a fast, very wide road queueing into a narrow intersection.)
Cutting the route can "solve" the problem by eliminating that particular congestion source, but only in the case of an extra, redundant shortcut route.
Other options -- like rate-limiting at the start point, or queueing separately for the shortcut route (an express lane), or forbidding queuing on the main road for the shortcut at all, both fix the general case and this case in specific.
The general version of the issue is: When you build a network, never queue in the core. Either drop traffic early and often at the point of congestion, or rate limit as close to the source as possible. Or change links at random and hope your network reconverges into a less broken state, I guess.