I think the downside is really cost, effort, potential contamination, and potential flavor impact. I have had one or two batches refuse to clear and only one of them had any wheat in it. I've had a Belgian Wit become clearer than Coors light by leaving it in the cold for two months. The ironic thing is, I hardly ever use any finings in the boil. My regular process is 10 days primary, sometimes a few days less if active ferment blasted through in 3 days. Primary for one week at ferment temps, then crash cool to 35F for another week. Rack to keg and put it on the gas. I try not to drink for 2 weeks. Prior to cutting a bit off my keg dip tubes, it would take at least those 2 weeks for pints to pull clear. Now that I trimmed them, it's clear by the end of the first week on gas.
If you're at the point where it's in the keg and it just won't clear after 2 weeks, I'd try racking it over into another keg through the lid. You might have a layer of sediment that the beer keeps disturbing on the way out. One way to test is to fill up your hydro test tube and stash it in the fridge overnight. If it clears, you know it's picking up sediment during the pour.
I'm more in favor of experienced brewers coming to the conclusion that they want to filter between kegs but I think most of the filtering questions are coming from noobs who bottled after 6 days in primary and one day in the fridge and wonder why their beer is hazy.
