"Like, between a 100-200$ blood test to prove natural immunity* vs. a free vaccine, it should make sense to get the vaccine."
The antibody test is about $45 from places like Labcorp. The vaccine is $40 per dose (so $80 total for most), with the government picking up the tab.
Yes, vaccination plus infection provides more antibodies. I'm not sure that it is correct to quantify that as "10x more resistance" as we would need to know where the threshold for resistance lies and all the factors involved (they don't know the min effective level of antibodies, and they are seeing protection in individuals before the antibodies are being produced).
"You don't lose anything by getting the vaccine..."
There are some people with valid concerns about the possiblity of autoimmune antibodies, which in theory, could be substantially higher if having already been infected. Sadly, I haven't been able to find any real research into this one way or the other.
"... they should be able to prove they have that immunity in the first place, ..."
Yes, other governments such as Isreal are issuing green passes for those confirmed to have recovered. I don't believe they are doing antibody testing, but we aren't testing vaccine recipients for antibodies either.