I understand what you are talking about, and you can still do that, but it is going to be expensive. Or at least, expensive for a typical 20-something heading out to explore the world.
Times have changed, and now like it or not, we are in the internet and smartphone age. The best travel deals are online, the cheapest accommodations are also found online. The Interrail pass is a bit of a relic, it can still be useful, but if you have no plan and limited cash, you are probably better off chasing last minute deals on your trusty smartphone.
And yes, I think we have lost something, disconnecting is hard, and stores tend to be all the same these days, and finding something interesting to bring back home is becoming a difficult task now that you can order everything online.
But I also think we gained something. The language barrier is breaking down. More and more people speak decent English as a secondary language, smartphones come with pretty decent translators, plane tickets are ridiculously cheap if you are not too picky. Getting in touch or keeping contact with people on the other side of the planet is almost too easy, great for exchange. When travelling in a group (even a temporary group), having mobile phones cuts down on the time waiting for people to gather, and offers more freedom than "let's meet at a precise place at a precise time", which is one of the most annoying parts of travelling in a group.
Now, I talked a lot about "cheap". That's because while travelling, I consider using money to be like cheating. You can do everything (well, almost) with money. Want to do a smartphone-less trip, randomly hopping into trains? You can, with money. Finding a ho(s)tel without price-checking online first? Sure, with money. Cheapening out is a good way to keep a "no plan" travel unplanned. But yeah, now there are smartphones involved.
And life is still beautiful. In my opinion, more beautiful than it has ever been, but in different ways.