This is the approach that Great Britain took.
As it turned out it may well have been cheaper than the Civil War.
Freeing the slaves and compensating their owners would have been cheaper than fighting the Civil War—but the owners did not want to sell (and a lot of non-slaveowners probably would have opposed spending so much tax money for that purpose). I don’t think anyone at the time thought that the federal government could compel someone to sell something if he didn’t want to. Until Barack Obama nobody thought that the federal government could compel someone to buy something he didn’t want.