In the most constructive language I can muster ..... poppycock LOL
Not only is mechanical filtration not important, let alone essential, I have found it actually to be counter productive. OK, maybe it's a somewhat different calculation for a FOWLR; but for a reef tank, particularly larger ones, the disadvantages outweigh the advantages. I do run a protein skimmer and chemical media canisters, both of which will perform some level of mechanical filtration, but that is not their primary purpose. Your poll responses imply your question is for purpose mechanical media, so I chose 'nothing'.
I simply don't have water clarity problems in my reef tank. Occasionally a coral colony spawns or I am forced to clean out the sump, but any attendant cloudiness soon clears - and the filter feeder inverts get a treat. I am sure things like filter socks do a wonderful job of removing particulates, also any zooplankters, but why is it necessary. When the lights go down at night, there are all sorts of little creatures that swim in the water column. Not sure why I'd want to filter these out. Natural reefs aren't cloudy, but they are also not lacking in small particulates in the water. I figure my UV kills enough of them.
Lastly, I really dislike rote maintenance tasks, so the idea of having to constantly clean filters socks is a big 'ol NO for me.