Do long distance through train ticket between arbitrary pairs of cities covering several countries exist?

In addition to Krist van Besien’s answer, one also has to consider a little known fact: in the EU, like for air passengers (the well known EC261), there are similar rights for rail passengers in case of disruption.

This means that if railways sell a single ticket from Seville, Spain to Białystok, Poland (a mere 13 trains and 34 hours!), if a train is delayed somewhere, passengers may be entitled to re-routing, assistance, accommodation and/or compensation. I think part of it is the reason for the question, but as you can see it goes a lot further than just allowing you onto the next train.

Like many airlines (mostly low cost carriers) which do not want to be responsible for any of this for connecting flights (which increases the risk noticeably when compared to a single flight) and for this reason do not sell connecting tickets (or pretend they are independent tickets with a “self-connection”), rail companies do not want to deal with this either, especially with extremely long or complex trips where a single disruption can result in extended delays.

While there are exceptions to these rights (each country can opt out for some types of services), it is far less risky for them if they avoid connections which are a bit too complex/long.

Some of the railway companies formed the Railteam alliance which delivers guarantees across their respective networks, which explains why you can book a single Hamburg-Perpignan (3 trains, 21h), Rennes-Wien (3 trains, 16h), London-Interlaken (3 trains, 10h) or Amsterdam-Milano (2 trains, 14h), but beyond that it becomes a lot more difficult, though there are exceptions (Stockholm-Milano: 3 trains, 28h).

Note that some sales channels also have an automatic limitation: for instance, the infamous SNCF-connect (French railways online sales channel) will not ever sell (or even show) a trip with more than 2 connections, whatever the railways involved (even inside France with only SNCF trains), which makes lots of itineraries impossible to book even though they are perfectly possible). I don’t know if they do this just for technical reasons (avoiding looking up too many options) or if it is because they deem such connections to be too risky.

In the USA, tracks are privately owned by companies that operate trains. Nobody gets on a railroad unless the track owner permits it. Obviously they allow themselves to run trains, but any other access is negotiated in free-market fashion, sometimes with a government nudge e.g. "we’ll approve your merger if you give BNSF access to Tucamari" or "if you buy into Amtrak you can quit the passenger business".

Europe considers this crass capitalism, and insists on open tracks. In theory, there’s a simple "free market solution" to your craving for meaningful international service. However, the "open tracks" idea is very problematic – there’s a reason North America doesn’t do it – and that’s even more so due to complex politics of the EU. Because guess who pays for rail upgrades – countries! This creates a "perverse" incentive to underwrite travel within the country, at the expense of international travel.

Even worse is the effect "high speed rail" has on each country’s domestic investment choices. France has a bang-up internal HSR system that is spectacular at connecting French to other French. Italy’s HSR is really good at connecting Italians to Italians. But what about those mountains between the two countries? Well that’s just not a priority. So HSR has actually been rail’s worst enemy, by functionally creating gaps in otherwise excellent domestic systems.

And North America has this same "domestic bubble" problem. Illinois and Michigan both have bang-up domestic lines, and Michigan even bought the track from Detroit across the state to Porter, Indiana and is HSR-ing it. But the last 100km into Chicago? Michigan’s not paying for that, and Indiana doesn’t need HSR going that direction. The Feds would need to intervene, and so it may be in Europe.

Now, Europe has gotten wise to this problem, and made real progress at deregulation and making open tracks work the way they’re supposed to. But the first bloom of deregulation really just resulted in popular domestic routes being doubled by discount carriers (however that has been quite good for rail overall; it hasn’t cannibalized the primary carriers, much the opposite, it has created new business by pulling new travelers and those abandoning airlines; and that "rising tide" has floated all boats – resulting in primary carriers gaining as well. But suffice it to say, the regulatory scheme is now a better fit for the market to respond to your international demand.

There are still technical issues, however, owing to incompatible tracks and trains. There’s a whole lot more to "interoperability" than just track gage.

In the past ticket prices in Europe were purely distance based. So all a ticket clerk in Oslo had to do to issue a ticket to Paris is look up how many km. that involved in Norway, how many in Sweden, Denmark, German, Belgium and France. Add up the costs of those segments and then he could issue a ticket.
I have spend time with ticket clerks buying ticket from my home town in Belgium to places as far as Rome, Poprad Tatry and Brest. Tickets were written by hand at that time, and it took some time to issue them.
Tickets were typically also valid for 2 months, so you take your time getting to your destination.

That changed with more and more trains requiring reservations, and having flexible pricing systems. A consequence for that is that to for example book you a TGV first a seat must be claimed for you in the reservations system, because only then is the price known. And that you have to do for each train with compulsory reservation. However the old system is still used too. If you for example book a trip from Gent in Belgium to Interlaken in Switzerland the system first will try to find seats for you on the Brussels Paris – Basel TGVs, and will then just add coupons for the Gent – Brussel and Basel – Interlaken sections, based on distance.

This makes it however a lot more complex to sell tickets, especially between railways with different ticketing philosophies.There are several sites that try to do something about that. One is https://www.international-bahn.de/en/ run by the German railways, and there are private initiatives like trainline.com.

Before 2020 you could buy a Moscow – Nice sleeper train ticket which would take you through Russia, Belarus, Poland, Germany and then into France.

Russian Railways had quite a few such routes, such as Moscow – Bar (Montenegro) or Saint Petersburg – Prague.

COVID put an end to this and the war supplied a nice tombstone.

There was also Moscow – Ulan Bator – Beijing train. This one may even run one day if China relaxes its COVID response.