That's an overly romanticized view. Moving long distances was slow and/or expensive. There was little in the way of international banking, so if you wanted to have money in your new home, you had to bring gold or silver or sell other things. If you were robbed, you were pretty much out of luck -- insofar as there were police forces, they weren't much concerned about foreigners.
It's true that you now have to cope with passports and visas, but for most places you might choose to emigrate to, you can expect a more or less fair police force, shops that will take your credit card, ATMs that will translate your money, and Internet to talk to people back home.
Well yes, I understand that this is the price of increased convenience for an average person. I simply feel that there's a certain sense of irony in those new barriers been erected as the old ones fall. Now it's harder to pull a Kosciuszko but easier to post pictures of your vacation on instagram, that's the trade-off here.
Before if someone traveled half way around the world to enter your country you let them in because clearly they were rich or industrious enough to get there in the first place. The deadbeats were excluded by the difficulty of actually traveling. Taxes were minimal and services were minimal so if you let a bunch of poors or refugees or whatever in and half of them did nothing productive it was no big deal either way. Now that any deadbeat can travel across the world and literacy/information is widely available (so the poor in country A know how good things are in country B) many nations have social safety nets countries try to pick and choose who gets in.
Edit: And before anyone thinks they're gonna score cheap virtue points by calling me racist/classist, I'm not using "deadbeat" as a dog whistle for any group(s). I'm talking about people who will be a net negative (definition is ever changing and subject to politics and whatnot) if they stay permanently.
It seems like you're the one trying to score 'cheap virtue points' by signaling your dislike of people you consider to be economic freeloaders to people of similar temperament.
One of the weaknesses of utilitarianism is that it's predicated on an assumption of reliable foresight that's not grounded in fact but is subject to all sorts of selection and confirmation biases.
It's true that you now have to cope with passports and visas, but for most places you might choose to emigrate to, you can expect a more or less fair police force, shops that will take your credit card, ATMs that will translate your money, and Internet to talk to people back home.