Haven't been on an Indian train for a long time, but what I remember growing up was steadily worsening service and performance, which I think has continued. Mainly a result of population increase and growing demand that is hard to meet. Something's got to give if it continues. This is based on fairly old information, but I'll try to keep my answer at a level where more recent details will hopefully not be relevant. Somebody correct me if some of my hidden assumptions etc. are no longer valid.

Given the decline, some sort of intervention is definitely needed, but privatization is definitely not the right intervention and would be politically infeasible anyway.

The key is to probably massively upgrade the road network (being attempted; progress is slow), strongly develop second-tier cities so there is less incentive to travel to bigger cities, thereby changing flow patterns, and fix budget air travel (currently in big trouble) thereby load balancing the overall transport network better and not demanding any one piece to serve too many market segments. It would probably also help to some extent to decentralize the governance down a bit to the state level so well-run states don't carry the burden of poorly run states.

This last idea is an unnatural one for a railway network, which is best organized by routes/corridors (example SE Railway currently connects the east to the south) rather than regions. But when there are huge performance differences that result from state-level governance differences, making state governments accountable for performance in their regions might help.

Right now, the Railway Ministry portfolio is one of the most desirable ones since it has a large separate budget and plenty of room for graft and populist politics that buy votes by making the infrastructure worse. It often goes to some regional coalition partner supporting the central government as a reward, and that partner then proceeds to mostly ignore national level railway strategy and milk the portfolio for regional gain. So one of the worst governed provinces, Bihar, has a history of using control of the railway portfolio to benefit Bihar at the expense of other states, and to the detriment of the network. Often the most toxic states are the ones that can benefit most from controlling the railway ministry and tend to fight to influence it (even when they don't control the portfolio), since they have the most opportunity for graft and political uses. So the problem has a vicious cycle embedded.

If states effectively had to pay for their portion of value derived from the network (yeah, tough to calculate... some complicated formula based on inter-state load patterns would be needed, perhaps modeled on carbon trading schemes), that might make them more responsible, and give other regions more financial breathing room to improve their bits. While "profitability" is meaningless for a social good with huge amounts of illegible cross-subsidies of various sorts, this would provide a rough equivalent. Two neighboring well-run states might decide to invest in a high-speed line and modern trains in a shared corridor, but not invite a corrupt third neighbor from the party. That might drive citizens of the corrupt state to hold their leaders more accountable. Speculative, idealistic thought I suppose, but I'd say the Konkan Railway is actually an example of this sort of thing.

Finally: modern subway systems. In my time, only Calcutta had one. Now clearly at least a dozen cities need good public transit with a modernized rail component where the local geography could make it work. This actually has much less coupling to the national railway network than people seem to think. I'd consider financially separating local operations entirely (it's sorta a mixed bag now I think... the newer subway systems are more financially independent than the older commuter rail systems). The only real connection has to do with engineering considerations like shared tracks in some areas and interchanges at terminals. Fairly weak and manageable coupling that would be beneficial to use as a separation point to break the problem down into smaller sizes. Integrated transport strategy (bus, cabs, train) is even more important in metro areas, and decoupling as much as possible from national stuff would help.

But an integrated national transport strategy with a governance structure that reflects and attempts to mitigate political realities is one of the toughest governance challenges to pull off anywhere in the world, and no large country has really pulled it off properly. So I am not holding my breath.

If somebody manages to properly improve and upgrade Indian Railways to be comparable to say, Europe's, it will be the greatest political achievement since, I don't know, the invention of democracy or something. It would make history as the greatest social-political-engineering achievement in history. Possibly more impressive than the moon landings.