Sure, but it still logically existed at one time and/or place in those worlds
I would say no, not always. A lot of fantasy settings don't have a historical progression modelled on real European history, and there's no particular requirement that they should. So it's not
logical to assume that. It's merely a
possibility. Plenty of societies developed with more or less use of forced labour/slavery. It's also interesting to me that some the most brutally slave-centric societies get like, ignored in the list of "slave-y" societies. The Vikings being a key one. Thralls were never a huge proportion of the population, but were a significant and noteworthy one, and sometimes they were freed, but that was hard slavery, no question about it. Yet you can definitely make a fantasy society that feels authentically "Viking" without using thralls at all - we know this because most fantasy Viking societies skip the thrall element! Including older ones (ironically this is more because people were either ignorant of the role of thralls, or trying to make Vikings look good, rather than out of any sensitivity or anything).
I daresay you could pretty easily make an authentic-seeming ancient Greek or Babylonian or Egyptian society without really having hard slaves either, just like oppressed workers and disenfranchised members of society, but who weren't actually owned.
Roman-style I think it's more difficult because Rome itself made slaves and enslaving people so central to its own worldview of itself, and that has very much propagated through history. People have tried but it tends to feel a bit more "fake" compared to say Vikings without thralls, even though both are equally ahistorical.
"Soft" slavery absolutely definitely gets a "pass" so yeah isn't an issue to have in a setting imo. Indeed we're actually at a cultural point where there's some excessive playing-down of how unpleasant some "soft" slavery* was (and from all parts of the political spectrum - not just the ends but also the center!). Just avoid the term slavery or any actual chains that aren't strictly carceral.
* = For example, re: indentured people coming to the US - people are like "Oh well they mostly only had 5-20 year indentures!" and that's absolutely true - but an
awful lot of them did not live long enough to see the end of their indenture (what was killing them - primarily disease, malnutrition/starvation, etc. is a whole other discussion).