I don't know about Chile, but I think the issue isn't so much the system being public, as in run by some form of government. Rather, the issue is in how "socialists" tend to run systems: everything is great until they run out of other people's money.
Now, I'm not in the "free market will solve all our woes" camp, either, especially when it comes to what we call "public service" in France. Over here, transit systems are facing a push from the EU bureaucrats for "opening up to competition". I'm bracing for the shit to hit the proverbial fan.
Sure, our national rail company is world-famous for being on strike all day every day and twice on Sunday. But, when they do run, they work fairly well and serve most of the country, including random, middle-of-nowhere towns. New companies coming in for the competition only serve the most profitable routes. Of course, I don't know all the laws, but I haven't heard of any obligation for new companies to serve the less profitable routes. So, the SNCF will have less money from the profitable routes to subsidize these lines. This means that either service will degrade, or the State will have to increase funding [0]. Now, I'm generally fine with paying (reasonable) taxes and whatnot, but I'm less fine with having to pay more taxes just so that some random foreign company can make money.
So, what will become of these people? When, at the same time, there's a push to restrict private vehicle ownership, and, especially, to limit access to town centers for older cars? Think these people can afford brand spanking new electric cars? Think again.
---
[0] I think the EU doesn't allow States to directly subsidize the rail company, it would be some form of unfair competition or similar. But the State is allowed to spend on social programs, so there could be some kind of program to help with transit, which, in the end, is the same thing: the people will have to subsidize service for less profitable routes because a chunk of the income from profitable ones has moved to a private company which doesn't care.
Look, if you're that uninformed, why bother commenting at all? Especially if you're in France, your takes on what constitutes socialism are weird to say the least.
SNCF operate those unprofitable routes in the middle of nowhere only because they get told and paid to do so by the state (Intercités) or the regions (TER). Private operators can bid to operate those routes too, and some do (soon Keolis, an SNCF subisdiary operated as a private company, will operate the first non-SNCF TER network).
Besides that, any operator with a license can apply to operate any route they deem profitable. And so far this has been a roaring success, with Trenitalia on Paris-Lyon (and now Marseille) and Paris-Milan being better and cheaper than SNCF. SNCF added low cost (Ouigo) trains on multiple popular routes mainly because they knew competition is coming (postponed by Covid), they probably wouldn't have bothered otherwise. This is a win-win-win for the average user.
The services that need to be maintained will be, regardless of who is the operator. Some of the profits of the private operators will pay for them (because they pay for network access, which covers the costs of the infrastructure + profit margin).
EU does allow states to subsidize transit (including trains) but the subsidies are subject to all sorts of regulations. They have to be of "public interest" and to not generate (excess) profits for the companies. At least in theory.