Why does the Empire maintain such strict border/inplacement controls? Shouldn't a libertarian polity have open borders?

Well, see here, for a start:

But a libertopia/ancapistan wouldn’t do $THING_THAT_THE_EMPIRE_DOES? - General / FAQ - The Eldraeverse

But, really, it’s not that hard to get there from here. The libertarian-proximal pathway to border/inplacement controls is observing that both rights protection and contract enforcement become much simpler if you can keep the goddamn barbarians off your lawn.

(There’s a reason noted by many cultures throughout the ages whose word for utopia, like “paradise”, means something along the lines of “walled garden”.)

Some anarchist-types think that you can deal with these issues one by one as they arise, but IMO, simple economic efficiency demands building a big goddamn wall-shaped metaphor, with the people you can trust with your person, your stuff, and to keep their promises on the inside, and everyone else on the outside, versus either ubiquitous policing or living with mass defection. It also helps - which isn’t strictly immigration policy - if you’re willing to kick out defective and defecting natives.

(This does not appeal, of course, to people who are not deeply invested in civilization and its many charming corollaries, but who gives a shit what people like that think? Besides, they’ll be outside the wall.)

To expand on the principles behind “keeping the goddamn barbarians off your lawn”, I refer you to a quotation I saw on Twitter way back in 2019 that sums it up in one:

Teaching people that benefits they are receiving as a result of them cooperating in a complex equilibrium are actually entitlements they should get regardless of their behavior is a great way to get them to blow up complex equilibria.