Entertainment There are days when absolutely nothing will make you happy other than the sound of a Harley Davidson motorcycle polluting the atmosphere in style.
To Impress People One of my favorite scenes from the book The Stars My Destination is when the protagonist, hiding in plain sight via enormous wealth (and in a world with mental teleportation, not unlike your story!), arrives at a social function in a railroad engine. People stood and stared as workers laid track to the door of the mansion so the train could drive up and drop its passengers. Think about it. Dang.
Because the Line's Busy Do you remember the good old days when the smallest emergency guaranteed you could't get through on your cell phone... or your land line...? It's nice to think your population of (I'm suggesting) 9.2 billion can open 9.2 billion simultaneous wormholes — but the reality is they can't (and shouldn't). Too many wormholes in too close a proximity causes bad things to happen. (And probably would in real life. That, or the current existence of one wormhole guarantees through the magic of physics that no other wormholes within a specified distance can be opened.) So, whadaya do when everybody's using the line? You get on your Harley, of course....
Because the Destination is Popular Even if your world allows any arbitrary number of wormholes to open in close proximity... that doesn't mean there's enough landing space for everyone! The 100th Marvel Movie (The Runaways save the world!) is opening at the Odeon and you absolutely must see it on opening night! The problem is, so do a number of people representing at least 700% of the actual number of seats in the theater. The result? Thousands of people trying to arrive in the same 500 square foot space — all at the same time. Gratefully, your tech simply won't allow the wormhole to form if there's not enough physical space to deposit you. So, you jump on your bicycle and hope like crazy you can beat at least 1,000 of those people to the theater! (BTW, if you think about it, this would be a very common problem at any goods distribution facility. It doesn't matter how big or small you can make the wormhole... there simply is only so much wormhole transit space to go around. Everybody else gets to use trucks.)
Your Wonder Woman Wormhole Bracers... Broke There ain't no such thing as perfection. It's pretty rare that the wrist controls for the wormholes break, but when your little brother swung the tree branch at you... well... Dad's not gonna be happy paying another \$1,000 for a new
cell phone set of Wonder Woman Wormhole Bracers. Bzzz, thank you for playing. Your consolation prize is you get to walk. (You can add to this one taking away your allowance, privileges, grounding you literally, or any other means of imposing reality on the unappreciative teen mind.)
There's Too Many People Near You You know what the basic problem with a rave is? They're packed! And in this city, raves are packed for miles. Oh, yeah! We're talking Zaphod Beeblebrox on tour! Woot! And you can't just open a wormhole in the middle of all that. You'd cut a dozen people in half as the event horizon formed. At least a dozen.
OK, to be honest, congestion (which at least three of these are talking about) will be a major reason why people don't use them.
You Can't Afford the Tech I don't own a \$1,000 cell phone, do you? Some people do, others take the bus. That's the circle of life.
Because Security Disabled the Destination And last of all — The folks over at Fort Knox takes a dim view of people trying to open wormholes into their vaults. I suspect there are all kinds of government, military, corporate, institutional, judicial, and who knows what else locations that absolutely, positively do not want your wormhole to open anywhere other than where they permit. Which can easily be believed to be "nowhere on this site." Prisons come to mind. There will always be the need for transport into and out of locations where security is a big deal.
I forgot one (or more)...
It Takes Longer to Teleport Do you remember that fabulous opening scene from the movie The Gods Must Be Crazy! (That really dates me!) where the woman gets in her car to drive 100 feet down the road to post a letter or some such? Yeah. Humans can be stupid. But she did it because it was faster than walking and cost her nothing to get in the car and fire it up. But, what if your wormhole has a minimum allowed distance? Or the time to form the wormhole is substantially (aka, minutes, remember the movie) longer than hopping on your bicycle? Then again, humans are creatures of habit! Maybe this isn't a good enough reason after all....