Technically 97.113(a)(5) takes care of commercial use where if you can use another service (aircraft radio, maritime radio, broadcast, CB, land mobile, whatever) then you're required to use it, and not use ham radio. Its to maintain the hobby-ness of ham radio.
WRT to your "administrative purposes" 97.219(d)(1) not only permits HTTPS and SSH, but requires it, in order to authenticate, presumably so unidentified or unauthorized people can't reconfigure your transmitter on top of the local air traffic control or something. Under 97.309(b) as long as you don't obscure the meaning you're all good. Obviously accessing administrative URLs is not an obscure meaning. Likewise tunneling a VPN trying to mimic administrative traffic to do illegal file downloading or something would be obscuring meaning.