I am not an expert in this area, but I think that blind/buried vias are more expensive because the board needs to go through drilling and plating multiple times.
it depends. The buried via's are typically done in 1 shot. so it's not like on a 6 layer they will bury 3 to 4 and 2 to 5. That would be very expensive.
The burieds run through the entire board and go from the first inner layer to the last inner layer. or the second inner layer to the last-2 inner layer.
if you then can get away with only having laser via's you are good. PCB manufacturers like laser via's. Why you ask ? because the laser can shoot up to a 2000 holes a minute with a much larger registration accuracy than a mechanical drill can. Drilling 3000 holes mechanically takes an hour ... and if the bit breaks and tears up the hole the board is scrap ...
To give you an idea : you need a 10 mil drill in a 22 mil pad just to allow for the mechanical drill to 'wander'
Laser via ? 5 mil hole in a 6.5 mil pad ... not a problem.
So in that respect : blind and buried is not really a cost adder , in volume it is actually the opposite. This is driven by the smartphone/tablet market. those are all blind and buried boards. they laser the outer layers. you can even stack via's on top of other via's using laser technology.
another nicety is that laser via's can be grown shut so you can put them directly in component pads.