@Mirikon
That depends entirely on the design of the space elevator - if it were in perfect equilibrium it would indeed just float there. More realistic it would be a bit unbalanced outwards so it can move higher loads and is more stable through the added tension. Cutting such a "rope" would turn it into a gigantic whip.
Micro meteorits will occur weather the base is on land or not, so no need to discuss that, really.
As for your other points:
1. In SR giant Aquacologies exist, so experience and ability exist either way
2. Only if you extend the cable into the sea. There is no need for this - a floating platform is sufficient
3. I think land access is still slightly more worrisome. It certainly requires a lot more sophistication for runners to organize submarines than accessing land locked facilities. If you add magic to the mix tunneling becomes quite easy actually and very hard to detect as you can't have spirits patrolling through the earth - under water you have much more options to detect intruders
4. That's true.
5. Tourists can use boats too - combining a luxury cruise with a visit into space sounds like just the right amount of decadence for the SR universe.
6. I'd imagine that ship inspections would be done at a safe distance - open sea would also allow you to use a lot more force to secure your site without having to worry about figurative (or literal) fallout that you'd have next to population centers. Also, you don't have to buy or rent land or have to worry about a government deciding to nationalize your property (less of a concern in SR, but still, a government backed by another Mega could do it)
7. A floating platform would also allow you to adjust position once in a while, either to compensate for sudden tension or to react to changes in the local geography (the environment in SR is a lot more volatile and a suddenly appearing volcano could be a real pain for such an undertaking, not to mention artificially induced earthquakes and other such problems)
The most common hypothetical or scifi designs for space elevators that I've seen follow the counterweight idea. In other words, you have a big object in space that is connected to a point down on the planet and the centripetal forces work to keep the line between them taught, allowing you to use it as an elevator cable. The fact that we know they captured an asteroid for the other end supports this hypothesis. Now, a counterweight needs to be connected to a solid point or it goes flying off like the hammer throw in track and field. Which is where the anchor comes in. The engineering requirements to tether a big rope to the earth are a LOT less complex than tethering it to anything remotely considered 'floating'. An artificial island works as good as normal ground for this. An aquacology could work, provided it was securely anchored to the sea floor, but you add in more points of failure there, as you add the engineering requirements of an aquacology to those of anchoring a giant rope keeping a rock from flying off into space in place. Wise man once said, "The more complicated the plumbing, the easier it is to stop up the drain."
A floating tether would be inherently unstable unless you were on a planet with no real tidal forces, without the ocean currents and storms you get on Earth. Consider the effects of a floating ship heavy enough to counterbalance a space station when it meets a major hurricane or a tsunami. Or what happens if some damn fool punches a hole in the hull, or lots of them. You already have problems with cargo ships being attacked by servants of the Sea Dragon. A ship that size could get her to be personally involved.
And you actually have a lot more options to find and respond to attacks on ground (or under it) or in the air, Jack. Drones are damn near useless underwater for the perimeter patrols you normally have them do on land. Water is quite good at blocking the signals, meaning you'd be trusting the dog brains of drones for your security on a multitrillion nuyen project where an attack would have the highest possible visibility next to a physical attack on the Corporate Court itself. Sonar is useful, but has been known to play hell with local wildlife even today. When you add in Awakened and Emerged wildlife to the mix (and we already know of Emerged dolphins hacking underwater systems)... well, you have a lot more problems.
And S-K is behind the building of the elevator. Putting a massive, almost certainly pollution spewing (this is SK we're talking about) megastructure on a boat is one hell of a middle finger to the Sea Dragon from Lofwyr. Which means you would need to add all her minions into the potential underwater threats.
Then you have the fact that you don't need THAT much more sophisticated an approach for runners to attack a floating structure undetected. Just running the underwater variables, scuba gear and demo packs could cripple a ship-based tether. Don't even need to sink it outright. Just disable some of the stabilizers as a storm hits, and you have all kinds of problems. Even if there isn't a second stage to the plan. Like I said, detecting attacks underwater is difficult. Aquacologies deal with it by being built like bunkers with only a few air locks, which have lots of sensors on them. This means they can concentrate on the main ways in, rather than having to guard against everything. Since they're anchored to the ocean floor, that works.
Having a floating tether if you don't absolutely have to (a water world, for instance) is literally begging for Murphy to show up.
Basically, aside from the benefit of being able to move it if Ghost Dance level craziness happens, the potential points of failure are much more numerous with a floating tether. When you're making a megastructure that is the first of its kind, and already has a lot of potential points of failure, going with a safer option seems best.
