Economic historians generally oppose the claim that slavery was unprofitable for slave owners. That is indeed the consensus, and has been since the 1950s. Econometric methods have moved on a very long way since then, but on this point little has changed. Alan Olmstead and Paul Rhode would tell you that, as would Gavin Wright. You also don't need cliometrics to come to this conclusion, because you can simply read the accounts of slave plantations to see that they were, in general, sophisticated capitalist firms ruthlessly managed with an eye to efficiency and profit, not quasi-feudal fiefdoms maintained against the profit motive out of sheer conservatism.

The question of "doomed to fail" is a more difficult one. Slavery has quite a strong negative correlation with future economic growth. So, while slavery may be very profitable for an individual in their lifetime, it is not a path from being a poor society to a rich one. Indeed, it is actively harmful for the underlying social changes necessary for industrialisation. Countries that relied heavily on slavery (Brazil, Cuba, Haiti, etc...) are not wealthy, and regions within large countries that made the most extensive use of slave labour (Southern US, Northern Brazil) are substantially poorer than regions that did not.

Does that mean "doomed to fail"? Fail economically, perhaps, in the sense of not developing as quickly. Whether slavery fails as a political project is a matter of politics, which has only indirect links to economic efficiency. If too many people, or enough powerful people, want the system to continue, there is no economic fact that will cause slavery to simply disappear. However, it is worth noting that no country in the Americas maintained legalised slavery into the 20th century, so there must be at least some reason why the case for abolition became convincing even to the Cuban or Brazilian state.