Street complete does load width - it can be quite useful for example for the fire fighters. They can try to plot some routes based on OSM data, then check if the narrow places are actually there and reach out to the city to address them, so their fire engines can get through.

That's a fair use for the data, but it would be hilarious if StreetComplete asked users to get a trundle wheel and measure the width of roads around embassies or seats of government...

There's a companion app, StreetMeasure, that uses Google's AR measuring capability on compatible phones. Personally, I carry a laser distance measure.