When they tested the MMU with the Space Shuttle in 1984
The astronaut was not tethered to the Shuttle.
I can see where once EVAs became more commonplace that having a
tether would become less necessary, and downright inconvenient if
you had to go a long way from the ship or station.
As for 2001, the thinking no doubt was that if Poole did get in trouble,
HAL 9000 would simply rescue him with the pod arms.
I did wonder why the pod was placed so far from the Discovery, but
perhaps that was to avoid an accidental collision between the two craft?
Even if Poole did have a tether, HAL would have still killed him anyway.