The Metro is an adequate commuter system to bring people to their jobs and home again. And, yes, compared to other US cities it's a beacon - but the US is a third-world country
and the OP, who's from Europe, should know it has huge limitations. Furthermore, speaking as a former DC and Silver Spring resident who didn't own a car and relied on Metro as my primary mode of transportation, I can say with some authority that outside of business hours - and particularly on weekends - it's a crapshoot.
You're totally right that DC is far safer than it used to be, but it needs to be said that random street crime remains extremely prevalent - far more so than most white, upper-income people in the city like to tell themselves. I know many people in DC who have stories of being held up at gunpoint in midday in places like Foggy Bottom, or being suckerpunched by a group of kids in Eastern Market. Even in so-called "nice" neighborhoods like A-M, there are often houses where shootings and muggings occur regularly but the city's dysfunctional laws means police take no action. I can think right off the bat of the corner of 15th/Columbia - literally a block away from embassies - as well as 17/Euclid, but there are many, many others. There are often shootings on the A-M strip - hell, there have been several shootings and stabbings at a club across the street from my old office, on 14/K right downtown!
I feel much safer walking around at night in Polanco, Condesa, even Zona Rosa than I would in A-M.
Anyway, I think we both agree that the OP is very unlikely to come to harm in DC. I'm just urging him/her to exercise more caution than s/he might otherwise think to do, even in apparently wealthy neighborhoods.