I saved 2 quarts of hop matter from a previous batch, so I could do some "testing" with the braid. Using 2-3 gallons of lukewarm water and a pint of the saved hop debris, I could easily see what was going on.
When just draining, and much quicker when running the pump, the hops fibers get sucked onto the braid, effectively clogging up the pores in the braid. When I run my hand or the stirring spoon along the braid, thus cleaning its surface, the flow increases momentarily, but clogs up again within 10-20 seconds. This confirmed what I expected to be the problem.
Moreover, I was surprised to see that it didn't take much hops fiber at all to clog it up. A very slight coating is all it takes to plug it up. While clogged as such, the resulting wort stream is about 1/8 of an inch, so some wort get through, but very slowly.
The good news is that the wort that gets filtered this way is very clear and mostly if not completely free of any hops matter. I assume only some of the finest particles makes it through.
To be able to run my (March) pump at all in this scenario, I inserted a valved feedback loop from the plate chiller's exit back to the pump's inlet. This prevents the pump from cavitating, by keeping the drain line, pump, chiller, and feedback loop full of wort. There is plenty of suction on the braid this way, just not much wort passes through.
I was looking to replace the braid with a bazooka screen or some other coarser filter mesh material than the braid. Hop bags, a hop spider, or a hop basket are among other options.