It's still state-run, and 90% of the reason why Deutsche Bahn AG is in such a sorry state is the German government. Want to see privatization done right? Look no further than Germany's southern neighbour.
In Czechia, the track (much like the highways) is managed by a state corporation, while the trains themselves are partly state-owned, partly private.
From my 25 years of commuting experience, the results are decidedly mixed:
* the track-managing state corporation, Správa železnic, is a shitshow that causes a lot of unnecessary delays by just ignoring needs of passengers and cargo companies alike; true bureaucrats,
* the highway-managing state corporation, Ředitelství silnic a dálnic, is very well managed by the latest director (Mátl) and really kicked off many projects in last years, which is notable in a very NIMBY-friendly country like Czechia,
* the state-owned railway company, České dráhy, used to be terrible, but competition forced it into providing quite decent services within last 10 years or so.
* the two main private competitors, Leo Express and Regiojet, are now visibly cash-strapped (esp. Regiojet), so the overall level of service has stagnated for several years. High costs of traction electricity don't help either. As of today, there isn't really a qualitative difference between boarding state-owned or privately-owned trains.
As you allude to, whether it's a public service or a publicly owned corporation is probably less important.
Switzerland just pays four times as much per capita for railway infrastructure.
And of course, it's small: a bit more than a tenth of the area, a tenth of the total operated railway length, a tenth of the population. There are economies of scale, but also system complexity that scales super linearly. Afaict, a train that takes four hours from start to finish is on the long side in Switzerland, not so much in Germany.
But I'm not saying that financing and management aren't the main problems. The current CEO of SBB has a background in computer science and railway transport. Many of the DB CEOs in the past 25 years had an MBA and a career in air travel.
From my 25 years of commuting experience, the results are decidedly mixed:
* the track-managing state corporation, Správa železnic, is a shitshow that causes a lot of unnecessary delays by just ignoring needs of passengers and cargo companies alike; true bureaucrats,
* the highway-managing state corporation, Ředitelství silnic a dálnic, is very well managed by the latest director (Mátl) and really kicked off many projects in last years, which is notable in a very NIMBY-friendly country like Czechia,
* the state-owned railway company, České dráhy, used to be terrible, but competition forced it into providing quite decent services within last 10 years or so.
* the two main private competitors, Leo Express and Regiojet, are now visibly cash-strapped (esp. Regiojet), so the overall level of service has stagnated for several years. High costs of traction electricity don't help either. As of today, there isn't really a qualitative difference between boarding state-owned or privately-owned trains.