[ThenAsNow]

Regeneratively cooling nozzles (i.e., circulating liquid or gaseous propellant in embedded cooling channels) is standard fare for liquid rocket engines. GP used graphite because it was a student project. Probably not what would be done for a real launch vehicle.

One thing to keep in mind about spike nozzle cooling is that you get compression shocks from the aerospike flowfield that strike the centerbody. These shock impingements drive up local heat transfer rates. As the flowfield changes with increasing altitude (decreasing ambient pressure), the impingement locations move. So when you size your cooling capacity, you have to account for this which tends to make the spike "overcooled" as compared to what you'd have to design for with the bell. This tends to correlate with increased pressure losses from the associated high coolant flow rates, causing a system-level mass hit and detracting from the nozzle Isp efficiency benefit. Take a look at XRS-2200 test video to watch the spike ramps ice over hard after engine shutdown. While not unique to that engine, the magnitude of that effect has a lot to do with how heavily cooled the ramps were.