The Case for One Bag Travel:
Less hassle at the airport: you won’t need to check bags or worse, wait for a bag from baggage claim, or THE worst, have a bag lost by an airline. Further, if you’re at a place - hotel lobby, train station, rental car parking lot, wherever, you won’t have as much crap to keep track of.
You’ll bring less stuff: that’s actually the point. Focusing on higher quality, more pleasing, more functional stuff will make your trip and your life better. When you travel lighter, you’ll worry less, move faster, and breathe easier.
Stairs, Cobblestones, Escalators, Subways, Trains, Funiculars, Buses, and every other travel encounter: If you are traveling light, you can deal with all the all the different situations you encounter with ease and style. Multiple bags and/or giant bags will always, always make these transitions and modes of moving more difficult.
The case against wheels:
The tripping, shin-smashing, extra-space taking. It could be that people with wheelie bags don’t understand how hazardous they are to others, or how annoying it is to give that bag a whole separate person’s worth of space in a line or in the plane/bus/train aisle.
Hands Free is the way: with a wheelie, you’re leashed to it like a dog.
Stairs, Cobblestones, Escalators, Subways, Trains, Funiculars, Buses, and every other travel encounter: Wheels don’t travel well over these things, and thus have to be carried onto them, defeating the whole purpose of trying to travel light. Did I mention snow? How about water?
And there's plenty of other travelers out there who have written about how wheelie bags are annoying and rude: