I think there are problems with that argument:
1. the higher speed increases the collision energy and so the damage done on impact by more than the reduction from those improvements.
2. often a new road now is an addition to the old one, not a replacement. In the example used, I believe it is still possible to drive through Newbury on the older bypass. The older bypass was a replacement because driving on the original high street is now discouraged and maybe closed to through traffic or even all non-residents. So in order to secure the safer road is used, should the older bypass now be closed to non-resident through traffic perhaps? Put a number plate reader on the river bridges, allow locals to register their vehicles, but anyone else driving through must pay a high penalty.
There are also some problems with this first argument:
1) The bypasses often are dual carriageways replacing a single carriageway. Therefore the probability of a head-on collision becomes very small. Cars driving in the same direction have a relatively small speed difference and thus the energy is not as large. Also there is more space to change direction if needed without creating a head-on collision.
2) Bypasses have no or at least far fewer pedestrians and cyclists, so the most vulnerable road users are not present.
3) As mentioned by a previous poster, standards are better.
Because of these reasons motorways and dual carriageways are the safest roads.
With respect to your second point, it would in my opinion always be good to discourage use of the road that is bypassed. The whole idea of a bypass is to guide traffic around a town. Depending on the local circumstances, you could for example close a tiny part of the road at the strategic location to make sure through traffic cannot use it. Also traffic calming and narrowing might help by increasing the travel time of the old route.