Taking it into simple investments and returns, slavery at the time worked, and unfortunately it still works today, it is still with us.
The balance today is between the cost of investing in labour, and the cost in investing in technology, which has been true ever since profit and gain were around.
If you can produce even an expensive machine to replace human labour, it is generally useful to do so, and the higher the cost of that labour, then the greater incentive for investment, innovation and invention.
In slave economies, and I suppose in hired labour economies, investors have to decide on a balance between short term costs and longer term investments, but the tendency in slave economies is not to invest in some uncertain technology, but to stick with what you know works.
Investment in technology very often brings unforseen benefits and discoveries and creates entirely new markets, in slave economies this diversity does not happen and will generally stagnate when faced with a more dynamic competitor.
Post war reconstructed Germany and Japan forged ahead of other European nations, and although these nations had the advantage of cheaper money, labour was in short supply which necessitated investment in technology.
The result was that in the UK, for example, where labour was plentiful and relatively cheap, companies preferred to continue with elderly outdated production plant, and products and the immediate returns on this minimal investment appeared very good.
I personally have operated steel bashing plant in a suspension spring manufacturing plant that was nearly 150 years old, though it had been converted from using the old overhead drive shaft power system to electric motors.It is easy to get good returns on equipment that paid for itself over 140 years ago!
It took 20 years for Japan and Germany to rebuild, but their economic performance since then speaks volumes.
Slavery in the US, and even in Rome, damped down innovation.
Why construct an expensive machine that can carry out the task of a thousand workers when your short term direct labour costs are free ?