A few thoughts not covered yet.
First, instead of people, a great first market for this would be cargo. It would enable same-day delivery of goods anywhere in the world. Surely there's a market for that. I know for a lot of tech gear, when you need it, you need it right now. Factoring in the cost of a business-class ticket (per kilo), isn't anywhere near being a show-stopper.
Second, time-to-load could be a real factor, especially if you have to reach city center, then load into a boat, then go to the pad, then load in the rocket, then wait for fuel loading, etc. A better way to do this would be to use hyperloops in a spider fashion from the launch pad out to several of the burbs around the city. I could see the hyperloops ending underwater near the pad, with a nice mall and places for people to wait until their rocket was in position for flight. God help us, you'd still have the TSA nonsense.
Third, it just shows a barge, but this would be an entire "thing" -- launchers, rockets, fueling stations, malls, security, and so forth. Maybe cargo is a pretty good way to get started. Adding people just makes the complexity worse.
Fourth, before you do cargo, you could do a few high-profile people shots every month, for folks with lots of money who want to be remembered as some of the first folks to ever travel sub-orbitally. Hell if you'd want an accident in those days, though. Public relations will be a bear. It reminds me of the early days of flight, when most folks had a deep and profound fear of the machine. Do you want to get on to the top of a huge stick of dynamite? I do, and most HN'ers might, but a few YouTube explosions that kill people could shut the entire thing down (or worse, delay it for decades)