Increased traffic on a road not meant to take it indicates some unmet demand, but it doesn't necessarily follow that the correct response is to accept the traffic on that road. It may be better to open things up elsewhere.
Also note that it's possible for adding routes to reduce efficiency, and thus for removing routes to increase efficiency: https://en.wikipedia.org/wiki/Braess's_paradox
Finally, there's the problem of externalities. Road traffic has costs to the people nearby, in terms of noise, pollution, and danger. The drivers don't experience those costs, and rarely factor them into the decision of which route to take. Putting a lot of traffic onto a residential road not meant to take it can easily be a net negative.