I guess an important thing to add here is that each of those computer systems can do exactly one of those tasks well. A single human could do all of them to a respectable degree. And then drive home then make a sandwich ready for tomorrow because she doesn't think she'll have time in the morning.
My day job is writing trading software, specifically for exchange traded instruments (shares, futures, options, some spreads, and a couple of other things). We (and a few of our competitors) DO use (k, m, b) for (1000, 1x10^6, 1x10^9). Our system has configurable per user and per group limits on the number of units or the value of the trade - specifically to stop this kind of thing from happening. I find it unusual that a trader would only deal in amounts of $100m for shares though, this tends to be more for FX (foreign exchange) deals doesn't it?
But I pretty much agree with you here though, there's a whole load of controls to stop this from happening. The are a few other possibilities other than a fat finger (or cat) but the one that jumps to my mind straight away is an algo gone wrong.
The short answer is money.
The long answer is that traders start at 7am by reading reports and recomendations.
They traders make decisions about what they will trade and what position they will take early on based on this information.
They will pay a LOT of money to money to get this information as early as possible.
The information providers want to be able to sell this valuable data and analysis.
This won't affect day traders so much, who try to squeeze trades in between the various peaks and troughs in prices during the day (playing with graphs basically).
What this means is that the people that are releasing this information will only have to wait until 10am and the information will still be released into the public domain that morning anyway.
It is is very important to trades who are trying to take long term positions and want to get a price that makes it worth while to trade the stock. (if you have to pick a trader take side with this is the one you want.)