Reasons for doing is good. Purpose for doing is better. As long as the reasons and purpose don't instead become an ever increasing restriction, to the point that a CG becomes an encumbrance purely to serve and become a slave to a mechanic, rather than mechanics serving a goal, sure.
I can see how a changing story that feeds a CG would be great. Broader rewards such as temporary discounts, or broader availability of engineer commodities (etc) can only be a good thing as it broadens the appeal. But just like being re-directed mid-mission, such as on arrival at the destination sector, such shifts have the potential of more of an encumbrance, than not. Lore can equally be used as a mallet, as it is context.
Broader rewards, broader goals, etc sounds great, that's a pretty decent QoL improvement and really just is more inclusive. Sounds good to me.