What they are asking is for NY to bid this, fight the bid appeals, contract this, manage this, supervise this, etc. Govt does not do well with new stuff, and everything goes through the big bureaucracy.
And vendor side, all the requirements (the forced source hiring so you can't use your own staff, but have to wait forever for someone to send you some folks for the "entry level" positions you are required to fill from the pool they have, plus a billion political football things that you need to jump through that have no real impact on the actual project etc) means the bids are high.
As someone who has worked both sides of this - the lack of knowledge here is shocking.
I'm not in NY, but looked up just the fringe overhead rate - 62%. That's probably double the private sector as a point of reference.
So to digitize 100 years of irreplacable records, be on-site, probably have to offer to leave the machine and equipment, work around a potentially unionized workforce (trust me - no fun). That get's costly.
If Ancestry shows up with insurance, money, references and experience doing this, they definitely would have moved to front of line.
People also don't realize that most of the gadflys involved in bothers government wear everyone out there. There are tons of overblown drama from folks with no budget who are totally convinced the state is out to get them. That makes for some very jaded govt workers.