From personal experience, I can tell you that it is possible to assign at least some of the named settlers to at least some duties.
For example, here's a few assignments I have done before. A couple of these are still in place on my current game:
- Marcy Long: Farming (By the way, she's probably the "gripey one" you're talking about.)
- Jun Long: Defense
- Preston Garvey: Scavenging
- Sheffield: Farming
- Vault-Tec Representative: Trading Emporium (This is actually recommended, as he will become a "Tier 4" vendor here.)
Personally, I haven't encountered (or just cannot recall) a case where I've been unable to assign any settler to a duty of my choosing. But, I haven't really experimented much with it either.
It is conceivable that there may be some rules in place, affecting certain critical NPCs, in order to protect the story flow. But it would take a good deal of thorough playtesting to enumerate all those rules (determining which named NPCs can or cannot do which jobs).
The first case you give seems to be one of the most likely ones to get blocked in general though. You're trying to assigned a named NPC as a Provisioner (that's what people running the Supply Lines are called - more on that shortly). That's something you generally wouldn't want to do to a named NPC - both in gaming terms and in programming terms - for two reasons:
- Provisioners are unavailable to the player, or at least difficult to locate, most of the time as they are constantly physically traveling between the endpoints of their assigned Supply Line. This is fine for generic NPCs, but most named NPCs need to be readily accessible to the player (and at a player-predictable - sometimes even mission-specific - location) at certain points in the game.
- Provisioners actually get renamed to "Provisioner". That's okay for generic NPCs who would just be named "Settler" to begin with. Not so much for named NPCs. It may just be easier or more efficient to program named NPCs so that they're excepted from selection for the job role, rather than to program their exception from the rename. Or this may not have even come into consideration, given that #1 above is a pretty strong reason to block them from the role on its own.
At this point though, I'm just speculating. I have not yet tested assigning a named NPC to a Supply Line. If I get the chance, I'll update this answer. (Or someone else who already has is welcome to.)
Tip: If you can, you probably want to avoid assigning named NPCs (especially companions) to stores unless they're "Tier 4" vendors. Otherwise, their normal dialog options tend to get in the way of trading a bit. Even some of the "Tier 4" vendors have this problem (The one mentioned in spoiler text above still makes me wait through his rather long ambient ramblings before I can actually Barter with him.) but at least they make it worthwhile.