Which sites do that for any meaningful reason? I see this argument often, but have a hard time either coming up with an idea of a business for which it would be non-marginally profitable or finding a real app/site which does that to cover the last mile of its world-wide scale.

Until that I believe this argument is equivalent to “what about Mars”. By supporting dead slow connections on Earth you simply support them to remain so.

As someone who has shipped thriftily-sized sites targeting developing countries, what you're describing is a needlessly extreme optimization. Inlining 3kb of data vs. 13kb would be a nearly unnoticeable difference for even the worst connections – like in Guinea, whose median download speed is around 3mbps.

Inflating the document size does impact paint time, but it scarcely matters here.

Bad advice.

You don't embed same piece of code on every page request but instead you make the code cached on first download.