The New U stations are clearly a gameplay element not a story element. The Hyperion voice has some amusing and relevant quotes but there is no apparent story link to the New U stations. They are never mentioned at all and the story plays out as if the New U stations do not exist (no one respawns except for the PC Vault Hunters). No one else, regardless of apparent monetary worth, respawns (except for bosses and mobs, which are again gameplay elements and their apparent immortality is never referenced directly story-wise).
The only in-story reference to the New U station existing at all is during a 4th wall breaky tutorial in Borderlands 1 with Claptrap. Other than that there are no references to the New U station whatsoever; they're not even lampshaded in BL2 (except by the New U voice herself). They're just sort of a necessary evil and the writing seems to quite deliberately not refer to them at all.
There's no reference of respawning at all either; story characters always act as if death is final (someone in Sanctuary exclaims "You're not dead yet? Alright.") And certain story characters' deaths/faked deaths. Even Hyperion workers (who would hopefully be allowed to respawn by Hyperion tech) either jovially or grimly acknoledge their fellow Hyperion employee's deaths (HE WAS ONE DAY AWAY FROM RETIREMENT).
Also, if you listen, the Hyperion lady from the New U station is quite happy to take your money; she has several quotes alluding to such and even thanks you for your "revenge quest" which brings them in lots of money in a specific quote.