But you miss the larger context, overlook that other approaches would also benefit from this, probably not making that much of an impact on relative competitiveness. What I'm also saying is they don't exist in isolation from the rest of the world (soooo... for example, yes, weapons; many more impactors - and you can't prove much with hypervelocity impacts - "oh well, another small asteroid hitting big target"; or: in-situ manufacturing tech would be viable at lower level of sophistication (more massive), while still probably ending up smaller and spawning colonies much faster than a ship which aims for providing comforts to largish crew)
Most importantly: even I think about "really powerful" lifting, I'm not thinking "magic" - but something which is still plausible
...so, it would need to be non-rocket based launch to LEO (which wouldn't bring quite the kind of changes), not strictly "engines" as imagined.
(and yes, when talking about the "magical nanotech" variant above, I treat it only as a possibility
which doesn't appear to be contrary to what this universe really is - it's quite lonely in that among most scifi fantasies)
Mass driver of some kind looks like most plausible (other proposals tend to be too silly even as far as mega-structures go), launching pellets (likely still not entirely non-rocket based) carrying small
parts (just to assemble one 10k in LEO?); maybe something like Startram (and probably only its smaller versions - meaning, passengers would still have to go up on, at most, a version of "pellet" which is very akin to present launch vehicles
Anyway, I think you're severely overstating what 10k would give. Nearest analogue is probably such submarine
at best, ~= at the largest (but probably closer to Kilo class, type XXI u-boot, Kobben, or even VII) - considering, cargo, landers, propulsion and fuel
(...oh yeah, it would need to have its own to take it out of LEO, and lots
of it: direct Hohmann transfer orbit from Earth to Jupiter takes roughly as much delta-v as launch to LEO itself - I assume you don't like the idea of long
trajectories via gravity assists).
So "low cost" is an understatement, probably an order of magnitude more expensive than most expensive subs (and they're... too expensive, there's plenty of efforts around to lower their costs while at best keeping the capabilities), imposed by the much harsher conditions and without the convenience of being able to surface to safety at moments notice; things are harder in space... lack of efficient cooling method for one. Propulsion is also much easier, no need to carry reaction mass (which would be likely a majority of the whole, together with the engine)
Typical subs also have way too large crews & little automation, we don't have the required tech here (it's again much harder when you can't just surface); "largish" crew variants would still be fairly small by necessity... travel time would still be long
(so... somebody might take a stash of embryos after all, tens of thousands could be less massive than one crew member; then somebody might realize this crew member wasn't really needed after all, and maybe another, and so on)
And that's ignoring cost of operations
...which, really, boils down to "OK, but what would you be doing 'there'?" Well, all we do boils down to resource gathering and manufacturing.
And I assume fancy 10k would be meant to return
...but what for?
And the thing with radiation was how fiction badly influences our imagination - as depicted
they offered virtually no protection (and BTW where were the radiators? At least Avatar does their size decently, as a starting point
Bases on the Antarctic essentially have this model: 10k+ vessels, no problem with propulsion, everything carried there.
...but, after a century, our presence and activities are minimal (probably less
than when we exploited the area, before we essentially exhausted the exploited resource
...all of them depending upon existence of life
BTW). Few thousand people in best of times, 1k when worse.
And antarctic is insanely more hospitable than outer space - still, no native human population.
Yes, one can say that we self-imposed "hands off Antarctic" on ourselves by treaties
...but those treaties are a realistic option precisely because
the conditions are so unfavourable. Our tech doesn't really work even there, our fairly expensive presence relies on constant stream of support.
I guess it will start with something like moon bases, probably largely / exclusively robotic for some time
...some scientists will want better
things, more than they can get funds to supply, so they'll figure out a way to utilise local resources - for some telescope probably, at first structural and ~passive elements.
Over time, people will pick it up, and take it further. Organic and gradual (oh, and no need to worry about most of the pollution and such in those manufacturing processes, they will be more efficient).
At some point, we'll realize we don't really need enormous launch capability.
1. Unless, yes, we would build a mass driver in, say, one of Lagrange points around Earth
...BUT, AGAIN, ONLY SMALLISH SLUGS THEN (and it also gets into "what for?" vs. building things in-situ).
Oh, and so it wouldn't really solve the problem of landing... (except by wasting lots of fuel for deceleration - and on Mars nearly hovering before
entering the atmo, which wouldn't scale the cargo that much)
But maybe we shouldn't want to all of this, consider some deeply disturbing and unavoidable effects - do you really want some large (multi-km, unfolded ~"metalised film" on light & redundant skeleton) advertisement ruining evening sky?