This power would be extraordinarily useful. Anywhere this person has ever been, they can make "anything they touch" appear there.
Convenient death trap: arrange to send folks to kill zones
Make an expedition to the North Pole (which will kill probably even many supers unprepared to be sent there in very short order). Take an airplane ride with a window seat, then simply teleport anyone the person wants to get rid of there.
Or just get a secret lair. Build a sub-sub basement. Surround it with chain link fencing, then flood it with water. Teleport people there to drown. Much less public that way. People just disappear and aren't found in spectacular, publicity-generating ways (like falling out of the sky randomly over the Midwest, or a huge pile of people killed via exposure being found at the North Pole).
If the user doesn't want to kill their enemies, and has resources, like they're Batman, build a prison. Hire a bunch of superpowered guards. Spend a few minutes locked inside a 2-foot by 2-foot square closet surrounded by powerproof glass, and you've got an intake cell where your new inmate materializes. Repeat, and you can handle multiple incoming bad (or I suppose good) guys simultaneously.
Anywhere the user has, or might have ever, been is not secure
Anywhere they can break into, or might have ever broken into, is not secure. Any place they might have flim-flammed their way past the front desk in disguise (think civvies), even briefly, is not secure. Any place they've ever worked cannot be considered secure. Note that the list of such places is vast because you won't know where they've been. This remains true as long as they live.
They can take a tour of the White House, even the unsecured parts, in disguise. Twenty years later, they could decide 'screw this, time to assassinate the President' and now you've got a problem. They can take a job as the janitor of an office building where someone they're targeting works. Failing everything else, they take a job working for these guys and then pretty much learn how to get anywhere they want.
Seriously, watch the video, it exposes how much even 'secure' locks mostly aren't. All this person needs to do is pop a door when nobody's around, or maybe when people are around and you just do the 'elevator repairman' schtick (again from the video).
TL;DR - This person can get almost anywhere. And if they can, then anyone who can engage their services can also. If you want in, and either can pay, or convince them to help you, a plan can almost certainly be arranged to give the teleport user the ability to get your entire crew in. This person can also assassinate a lot of folks by finding their office, then teleporting hand grenades or nerve gas canisters or even assassin droids in.
Devastating force multiplier
Combat effectiveness is not all about kicking ass and taking names. Some things don't directly bring the thunder, but are good at making the thunder your other folks have got more effective. The military has a name for this; they call it a force multiplier.
In addition to the direct usefulness of teleportation in a fight (being untouchable, being able to kill at a distance, being able to take people prisoner just by touching them, etc) teleportation is a devastating force multiplier.
The way you have set this up, teleportation is a highly effective force multiplier, because the teleporter can bring a whole team of capes along for the ride. And they can get to the scene much quicker than if they had to take the Batplane or whatever. As established above, if the teleporter spends a lot of their time travelling around, considering it their job to spend a lot of their 'off' time expanding their potential teleportation destinations, they (and their backup) will be able to almost instantly appear to disrupt the plans of their adversaries.
Instead of being able to count on it taking (say) between 20 minutes and an hour after the alarm goes off, until the Superfriends show up (because even if they're all on duty right that second they still have to physically go to the place), with Mister Panopticon on their side, they can appear in under a minute. I.e. if you want to attack something they care about defending, you have to assume they will be on you immediately. Smash-and-grabs, where the idea is you're gone before anyone shows up, are out.
Likewise, if the Superfriends want in, you have to assume they can get in anytime they want with no warning. They will simply teleport a whole crew of heavy-hitters somewhere inside your security perimeter. You can't rely on being able to buy time, keeping them tied up at the front door so they don't get into the sensitive parts of your facility. You can't really have a security 'perimeter', you have to have very high security basically throughout any facility you want to keep these folks out of.