Answer 1 - Magic cannot teleport objects.
The puzzle is a physical object. A soul isn't.
Magic cannot teleport objects. Otherwise why later in battle city did Marik play Yugi with a physical Slifer deck instead of just playing remotely and then teleporting the cards eg give Slifer remotely if Marik lost?
From reddit user The_Doolinator here:
Honestly teleportation seems to be a very rare, almost nonexistent magical power (I think Shadi is the only who utilizes it, and I’d chalk that up more to him being a spirit. You could make an argument for Bakura too (the ring rematerializes on him after he was separated from it) but he is at least part dark god so there’s that).
So yeah, teleportation is probably just not a power normally at the disposal of other item holders and those able to use it are tapping into something specific to them.
Or the real reason: powers as the plot demands.
Answer 2 - It was a dub thing.
From reddit users
tokarooni here:
Pegasus wanting the puzzle was a dub only thing. In the original he just needed to beat Yugi publicly as part of the conditions for taking over Kaibacorp.
Verificus here:
Pegasus didn’t want a puzzle or soul in original manga and original anime. Just something 4kids added.
MaCl97 here:
he never wanted it in the manga. He just wants to beat the guy who beat Kaiba and take over kaiba corp. Marik too, he doesn't want the puzzle. He just wants to kill the pharaoh.
Source for Answer 2:
See for yourself in episodes 35-39, a sub-arc called Match of the Millenium, specifically the middle episode, episode 37 (fandom doesn't point this out though). There's a part in the 4kids dub just after Yugi and Atem destroy the toon monsters and just before Pegasus makes the game into a shadow game where Pegasus says like 'if I win, then I plan to claim your puzzle.'
Compare the original anime, the original Japanese manga or even the Singaporean dub. There is no such thing that Pegasus says.
See here (22:00 - 23:40) for example in the original anime. Pegasus acknowledges Yugi and Atem have a millennium item, but Pegasus doesn't explicitly express any interest in claiming the millennium puzzle.