"Belgrade to find 0 hotel rooms due to a football match."Once, I had the same problem due to a football match in Rome. In hindsight, how I got a bed for the night was hilarious but it wasn't at the time as I was dead tired (I'll spare you the details—I learned quickly that very strange things can happen in Rome).
A day or so later I was on a train from Rome to Vienna, the trouble was that by then many of those football fans were returning home so we all ended up together on the same train. To make matters worse, many of them were drunk. Suffice to say, Austrian Customs and border police were not amused, the train was delayed many hours.
See, you're not alone, we all have days like that when traveling in strange places especially so when crossing country borders.
"I love trains. But the process needs improvement, just like airplanes. Long-distance travel without a car is honestly quite difficult in Europe and USA imo."
I agree with you about the US and Eastern Europe, however you really shouldn't have any trouble in Western Europe—France, Belgium, Luxembourg, The Netherlands, and Germany—even Italy (if you're forewarned what to expect). Of course, here I'm referring to major towns or ones that receive a reasonable number of foreign tourists. As always, small villages and places that are way off the beaten track will be difficult no matter where you are (so are one and two star hotels problematic in such places as they are much less likely to speak English).
In particular, I found such travel by train in the US much more difficult than in Western Europe. It seems to me that since WWII all the once excellent (and traditional) railway infrastructure (such as railroad-owned hotels at or near railroad stations, etc.) has either been dismantled and or sold off, so one ends up at one's destination—even in large towns or cities—without any or minimal local support. Right, all this once infrastructure has been transferred, or relocated or rebuilt around airports.
I reckon the US will have a huge job in reversing the process (or duplicating the infrastructure as it once was around rail terminals), that is if it wishes to make rail truly relevant again.
Generally, Europe is miles ahead of the US in this area of public transport infrastructure.