So, I guess I might have a mission/role where a tanker "could" work.
The traditional role of the Lioness? Small Craft, I think that is the name, the 2 that escort Droppers from JS to Planet.
They mention that in many cases planets use Heavy Fighters for this instead of the dedicated Small Craft.
Now heavy fighters don't have the fuel to keep thrusting at 1G like a Dropper does.
Actually, I'm not sure that they even have the Life Support to pull it off.
But my thought is this.
In a scenario where you have Fighters at a Jump Point Space Station & also on the Planet, you might launch fighters w/ a Small Craft Tanker like the Wild Cat I mentioned above.
They would refuel them as the Fighters run out of fuel.
The issue is the week long times so my thought is this, you end up with 2 sets at the start & end point both.
A "Planet Based" formation escorts maybe 1/4-1/3 of the way & another group out of the Space Station goes out & picks them up a day or 2 out of the Space station.
This would, in theory, provide coverage from the most common locations where other ships might be based to raid shipping.
I mean, if its a week from Jump Point to Planet, the "4-day" mark at Turn-Over for the Dropship is going to be well outside the horizonal plane of most orbits I would think. So anyone raiding you at that point really would have to be just sitting in the middle of space powered down waiting for someone to pass by, maybe, if lucky.
Doesn't seem like a location that would have pirates to me.
Anyway this "hand off" type set up of escort out & escort in is going to be for areas that have fighters & tankers but not the dedicated "escort shuttles" like the Lyoness?
Another option is as someone mentioned, using the tanker in a SAR role to go out & refuel fighters/dropships that went "bingo" in the middle of a battle & drifted out of the combat area & need some juice to get back home.
Finally, maybe in a Strike mission type scenario where you absolutely don't want to have the Dropper anywhere near the combat (Like a Vengeance), you sent out a couple wings on a Strike assignment & the Tanker is there to refuel anyone that runs out trying to get back to the dropship.
Coasting in space is "free" but changing direction & any fuel needed for close maneuvering to dock would still be useful if you ran out I'd think.
And better to try to doc 2 fighter sized craft than a Dropship.
Also, trying to recover a full wing of fighters that are all bingo fuel & coasting is going to be a LOT of maneuvering for a single dropship.
Its not common, but, I can see where the existence of a tanker would be helpful.