They have 4"X4" along the edge of the slip fingers,
called "toe rails". So a looped end or large eye wouldn't helped the dock
person. For a quick tie up the bitter end of the line must be passed under
the 'toe rail'

In many instances, the line thrown ashore is far too long to screw around with
trying to pull the bitter end under the bull rail.

IME, you can get a pretty decent quick tie
by grabbing the line along its length and running it, doubled, around the bull
rail either side of a support block and creating the figure "8" you described.

However, no one ever seems to do this correctly and the line length, boat
position is seldom correct the first time, so I just let them tie or off
with a round turn, enough to hold the boat into the dock and do the final
adjusment myself.

Excellent practice no matter who takes your line or what type of system
prevails for securing same. :-)