I suspect that with many of the advanced players who buy a carrier, the carrier will become their "home" and everywhere else they'll be "just visiting".
I have a "home sphere", 25 LY in radius, within which I try to push my favoured faction in each system. I don't have one particular faction I favour, though I have one system at the centre of the Sphere I push more than others. I've worked this SPhere for several years now, and as a result I'm Friendly or ALlied with most of the factions there - even the Anarchies and other factions I don't particularly like and even actively oppose, because they keep getting offered as mission beneficiary targets for factions I do like and support.
It's often the difference between having an 800k transport run and a 5 million transport run on the mission board. The difference between missions at Cordial and at Allied is striking. And not only money, but more G5 mat rewards and more Rep+++++ missions too.
You'll find that "credits" and "other high-value stuff" are actually one and the same thing. A mission has a given "value" of reward, and that value can be expressed in several different ways in the two or three optiions given to you to accept. A standard packet of five G5 mats, for example, is worth 1.25 million value points. So if an Allied mission has a total of 2 million value points, the options it gives you might be 2 million credits (1 point = 1 credit), or 5x G5 mats and 750,000 credits, or 20 tonnes of Consumer Technology (at 6810 cr/t) plus 1,863,800 credits. Rep+++++ and Inf+++++ are also worth value, depending on the class of mission involved. Leftover value points, once the value of the special item is deducted, are converted into credits and this becomes the credits portion of the overall mission reward.
Low-grade missions never get up to 1.25 million points of value, so you never see G5 mats offered as a reward. Same as you never see Rep+++++ and Inf+++++ rewards when not Allied. The obvious exceptions are the occasional "follow-up" mission you might get offered, which are usually much more valuable than the standard missions.