In a later version, systemd v235, halt could be allowed without a password. In order to make it allowed, you would have to edit some polkit configuration file.
The description on the commit which added this feature for halt, says "the whole concept of halting isn't really too useful". I think this point of view explains the difference v.s. poweroff/reboot :-).
Another way to look at it, is that poweroff/reboot buttons are provided in common GUIs, and we expect them to work without needing a password. The systemd project is providing a way to implement this. But the user does not normally want a separate button to "halt".
I reviewed this commit and helped approve it. I felt it was generally safer for systemd not to change this behaviour, and there wasn't a clear reason for change.
The original behaviour might have been considered simpler... maintaining code and documentation for an API if we didn't actually expect it to be used can be positively undesirable. Or it might have been a way to block users from doing something they didn't actually want to do. I'm not sure. I very vaguely imagined one other concern. "halt" is defined to enter the ROM Monitor, if there is one. If there was some hypothetical ROM Monitor which required a password at boot time, I am not certain that it would prompt for the password again when the OS handed back control.
Adding polkit support in v235 was a side-benefit of making logind support halt. This was implemented to make
systemctl behave consistently for halt, but the polkit support wasn't really the reason.
 PR #6944 - "systemctl reboot/suspend tweaks" - commit 36b69c313120 - "logind: add Halt() and CanHalt() APIs"
You can see the polkit default settings in
/usr/share/polkit-1/actions/org.freedesktop.login1.policy. You can search for similar entries for
reboot, and look at their
<defaults> element. And in v235 and above, there will be an entry for
halt which you can compare.
You may notice some additional details. Like, if you have logged in over the network, the system will require an admin password to power off.
If you know the right incantation, you can create a file somewhere under
/etc/polkit-1 which provides a different setting from the default. My guess is you have to define a "rule".