And this does not even address the real problem - every imperial slave takes away a job from a free citizen. Why pay someone if you can use a slave for free? And the free citizen left jobless will likely have no option than to sell himself into slavery, taking away another job, and so on. And this is the real reason slavery was abolished IRL - it is a death spiral for economy, incompatible with a free enterprise system.
This would only be true if fresh slaves (say, from conquered regions) were being imported back into the Empire and creating a glut of available labour in a limited environment.
It could be that a 'job' doesn't change actual employee at all. Only social and employment status would. Most likely however, the job would be waiting for the slave somewhere else in the Empire.
There are jobs in most 'advanced' societies that most people don't want to do (I'm thinking of carers, cleaners, teaching assistants etc - I'm sure there are lots of others). Theses places are filled by economic migrants with a wide field of abilities. Isn't this actually contemporary exploitation by the global capitalistic system? Can't you imagine the same idea manifested in a different form, where instead of free markets picking and choosing according to profit margins, the society takes responsibility and ownership of the poor and destitute, giving them employment and the chance to work out of that poverty?
I like the idea that the Empire takes responsibility for it's population and then demands responsibility from that population, regardless of social status. I can really see such a system as working and benefiting a society that had the courage to do it.
The Empire, like other powers and even single system independents, are expanding into the galaxy. Job creation, at all levels, would be happening in this expansion.
If anything, it would be robots and technology that might take away jobs and livelihoods; something associated more with the Corporate mentality than Imperial prestige - and where is the honour in being served or serviced by a machine?