The amount of productivity I lose when trying to work this way, hunched over my laptop screen in a public place, is immense. An office, downtown or at home, is absolutely necessary. Are you a software engineer?
I am SWE and Engineering Manager. I find open offices to be way more distracting b/c people discuss topics relevant to me (project work or even good morning hellos).
Public libraries are quieter than my office and coffee shop noise is background noise.
Lack of external monitors is a fair concern, but I found external monitors to be too distracting. I only need to look at one thing at a time. I don't want random things popping up on the screen next to me.
It's not the external monitor I'm looking for. It's single monitor larger than a laptop screen and a usable keyboard. I fold my laptop screen closed.
Also, I want to be around for relevant conversations. Context switching is not an issue for me as long it's not unrelated to work (or something unobtrusive like "hello").
For me, WFH means I can walk/bike/drive to the local coffee shop or public library to work, but still live in a cramped studio apartment.