One likely reason is that the airport station is underground, with only two platforms, and has fairly a frequent service. So it might not have much scope for sleepers (which tend to have longer-than-average dwell-times, especially if they're - in effect - at their one stopping point for a capital city, which this would be). Whereas Hoje-Taastrup has four platforms and hence more flexibility. Also, for people connecting into the sleeper by getting a metro out from Copenhagen, I think the connection between the metro and the main-line station is tighter at Hoje-Taastrup - they're really one station (which isn't the case at Kastrup/Airport; both of them are there to serve the aiport, not primarily to function as an interchange between the metro and the main line).
There is an above-ground avoiding line on the airport route, skipping the airport station, which I presume is for freight between Sweden and Denmark, or maybe anything else not stopping at the airport (though I think pretty much everything does); it also - in theory - could provide a tighter connection into the airport's metro station. However, there's no platforms or facilities for anything to stop there, and it wouldn't make sense to build station infrastructure for just a handful of sleepers each day.