Yes, it is possible that whatever FTL tech they are using will work with a living creature but not with some machine. Maybe they just encode human DNA to clone for slaves because their culture does not allow them to use their own DNA for slaves, and DNA is easy to send over their FTL tech.

When discussing aliens you have to consider that their reasoning, their culture, their motivations, their technology, their customs, their values are all _alien_ to us. You have to be open minded, for every excuse we can come up with for "why not" there are infinite explanations for "why so".

The thing is that culture, motivations, and technology are all shaped by constraints imposed by the laws of physics, which (by definition) can generally be presumed to be universal. Having plausible explanations for "why so" doesn't change the fact that doing so would likely be so inefficient that it would place their entire culture at a significant disadvantage.

Yet on a cultural level, I think the "food/slaves" narratives of alien invasion are actually failing to be open-minded enough. Mechanical labor and physical nutrition are the kinds of things that our newly industrialized post-colonial societies worry about. It's not actually a particularly "alien" idea. Thinking a much more technologically advanced society would come to Earth for the same reasons comes across to me as projecting our own anxieties and sins.

I mean, maybe?

People still eat https://en.wikipedia.org/wiki/Ortolan_bunting despite the illegality, low nutritional value, and the ready availability of other options.