Long flights can be hell. Uncomfortable, terrible food, and even when you land you are so out of it you feel like crap. So imagine if you fight the battle of your life against E. Honda in Tokyo, and as soon as his body hits the floor you have to get on a plane and fight Ken in New York. That's like a 20-hour flight with super powered fights on each end. You would feel so awful you wouldn't even be able to stand up.
Whenever you go to a new country, you need your papers in order. Passport, immigration slips, customs declarations, etc. These are just a few of the hoops you have to jump through with international travel. When you are boarding the plane at the airport, they are going to ask you state your business in the country you are traveling to. Something tells us that "I'm traveling to Thailand to fight a 7 foot tall guy with an eyepatch" won't fly with the TSA people.
Unless you're a jerk, you love your country. All other countries are a bunch wussy weenie crybabies compared to your own. So when you gear up to fight in a global karate tournament, you should be flying your flag. But what if you lose? What if you train and train, and boast about how awesome you are with the hopes and prayers of your nation on your back, and then you get your ass kicked? You can't come home and say "Yeah, well, I got a few good shots in on that guy from Romania." If the World Cup has taught us anything, it's that even the smallest country can topple a super power. Thanks, Ghana!
You just had some girl kick you in the face like 50 times in a row. She tossed you to the other end of the ring and did it again until you turned dizzy. You quickly snapped out of it and ended the fight by cheaply kicking her in the shin until she dropped. Now, you have to head to your next fight right afterwards, with no time to heal. So what if you got fried by Blanka in your last fight and now you have to face Balrog's furious punches? You'll be starting every new fight at a disadvantage.
Most of us get like, what, two weeks of vacation a year, if that? If you went to your boss and said "I need a month off to compete in a world wide super fight," they might look at you a little funny. And then promptly deny you. Even if you GET the vacation time, you would want a few weeks of R&R to celebrate and heal your wounds if you win, right? What about guys like Guile? How could he convince the Air Force to give him the leave time? The simple answer is that they wouldn't.
We've all slapped a friend in a playful manner at one point or another. How about shooting fireballs or hurricane kicking one of them? Poor Ken and Ryu had to set their brotherhood aside and do battle until one of them fell. Can a friendship survive a Dragon Punch?
You have fought all over the world, fought a dozen of the hardest fighters ever, now you can bask in your own glory. But what if it's not what you were expecting? Look at Guile. You are a cold-blooded, round-housing, textbook ass-kicker and took on the whole world and won. You'd expect his ending to be him taking up a life as a badass mercenary or something, right? But instead we get a heartwarming moment where he is reunited with his little daughter, where he cries like a girl who didn't get a pony for her birthday. All this, and all he did for the whole tournament was taunt his opponents about being a family man.