Does landscape fabric (filter fabric) get clogged? If not, why not?
Think about how a coffee filter works.  You have a paper filter clogged with wet coffee grounds.  The water slowly passes through the filter paper and you have a thin film of water between the filter and the funnel.  That film from the entire surface of the filter paper flows to the bottom of the funnel.  By the time it all aggregates and flows out of the funnel, you get a stream of fast-moving coffee.  That's what goes on with the filter fabric and the drain.

The drain channel is sized to move water at a certain rate.  There is typically a perforated pipe that offers unimpeded flow to the water once inside, so it is quickly carried away.  The water gets into it by traveling through big gaps between large stones, and some of it even travels through the stone gaps.

If the drain system is at the surface of the ground, much of the water will get there by flowing over the ground until it reaches the stones.  Some of it gets there by flowing through the soil; flowing much slower, through much smaller paths between dirt grains, over a much bigger area.  If the drain is completely buried, like around the footers of your house foundation, all of the water will get there by traveling through the soil.

The filter fabric is porous, and acts like a barrier to separate the soil from the drain.  It gets clogged with fine soil, but not really different from the soil the water is passing through to get there.

So you have a lot of water collecting in the soil over a very large area.  It moves slowly through the tiny gaps in the soil, but that's a lot of water moving slowly.  It passes through the fabric barrier at the perimeter of the drain system, which has a lot of surface area, and the aggregated water becomes the stream flowing through the channel.

If filter fabric is only placed around the drain pipe, the stone in the channel fills with silt until there isn't really a difference between the stone channel and the soil.  The water moving through the soil will find its way into the perforations in the pipe, but you're aggregating slow-moving water from a few small holes, so you only get a trickle through the pipe.