The designs were revived in the 1980s by Gary Hudson and Pacific-American Launch Systems (Phoenix) and later by General Dynamics (Millennium Express --disclaimer, I helped name it) as their proposal for the DC-X competition.
Yes, New Shepherd was clearly influenced by all that (as have several others, including a Japanese suborbital test vehicle). The design makes sense for a number of reasons:
- structure weight is critical for SSTO, and the closer you get to a sphere, the better your structure-weight to propellant-volume gets, hence the relatively squat shape
- the rounded-cone shape makes a great reentry vehicle, with some maneuverability (assuming asymmetric mass distribution)
- the heat-shield on the base serves to protect against engine exhaust on launch as well as reentry heating
- aerospike nozzles are inherently altitude-compensating, so potentially more efficient
Of course there are downsides to the design too, particularly in terms of integrating the design so that it's light enough for SSTO, and starting and controlling the large number of thrust chambers (usually at least 16, some designs with 24 or 32).