If that wee true, since Starlink will reach everywhere, they would only need to fund Starlink. In fact the OP would be correct and no subsidy would be needed since Starlink is already being built.
For the avoidance of doubt, here's the link to the FCC RDOF auction and the relevant quote:
"... Rural Digital Opportunity Fund to bring high speed fixed broadband service to rural homes and small businesses that lack it."