Unless there is a legal aspect that I'm unaware of (I'm not a lawyer), I don't see any good reason for SE doing that beyond trying to control the narrative by selectively featuring their statement across the network, but forbidding mods from doing the same for the strike announcement.
[...] CMs will work with Moderators first before unfeaturing and should it be necessary to get a post removed from the featured list sooner than it would naturally age out of the cache, moderators can request help from the CMs to do so.
Removing the featured tag from moderator-endorsed posts doesn't really seem like "CMs will work with Moderators" - it seems much more like SE working against the will of the moderators.
Why are SE staff members un-featuring posts about the strike and violating SE policy?
*A diamond moderator left a comment on MSO indicating that staff were un-featuring these. That said, this was not shared by staff themselves?