The escapism and power fantasy intrinsic to the genre combined with modern anime being designed to appeal to the type of otaku who'll spend hundreds on merch or dvds (or $40k on a statue of their waifu). For these types there's an appeal in a girl who literally can't leave them, hence slavery. Harems are partly wish-fulfilment, partially marketing: 5 archetypal waifus will appeal to more otaku than 1 archetypal waifu.

We started off with Magic Knight Rayearth, Escaflowne and Fushigi Yuugi too how did everything go so wrong (answer is capitalism, duh)

Ok Fushigi Yuugi could be pretty problematic at times but still!

There are a few proto examples from western Baentrash fantasy like The Radiant Knight (do not read) that got picked up where the power fantasy (that was already being deconstructed in novels like A wizard in spite of himself and The man who came too early.) was mixed with dumb horniness.

As the chan culture picked up and became more right wing and misogynistic both here and in Japan, this went from moderately problematic to a death spiral dropping all the cool social history and cultural/psychological examination parts of portal fantasy in favour of having a little world that you get to do free war crimes to but it's good actually.