I'm not sure that you understand exactly what a Starlink gateway does. The gateways in your first link don't connect end users, as you said, they link satellites to the rest of the world's internet.
The satellite is the equivalent of the cable from your house to your ISP (assuming you use DSL), and the Starlink terminal is the equivalent of your DSL modem, and the gateway is your ISP's server. Your computer will establish a wireless link to the satellite via the Starlink terminal (yes, it's just a box and a dish antenna as simple as in the link I posted), and the satellite will connect to the gateway on the ground, either directly or via other satellites, which are located in the US or other countries, but not in Taiwan. The gateway does look complicated, but it is not directly related to the end user, just like you don't need to worry about your ISP's server room yourself.
I'm sure Starlink's internet speed can't be compared to a typical VDSL or fiber network, but we're not talking about enabling Taiwanese users to watch 4K TV episodes on Netflix even during the war here, the bandwidth provided by Starlink is more than enough for the problem we're talking about.