in the posted picture my beer was in fact ice cold, the fermenter was at negative 1 before i filtered it. it was however not carbonated. mind you - i've not noticed that dissolved co2 makes a beer cloudy.
anyway - i have no interest in the filter or dont filter debate, its been done to death and people can decide for themselves.
As to the OPs whether it costs or saves beer question - I manage to get a bit better use of my beer if i filter. the filter means that you can continue to run to your keg even after gunk starts to come off the yeast cake in the fermenter, either primary or secondary, in fact if i am using (i rarely do) a secondary, then i would probably swirl it up when it was getting close to empty and run every last drop out of it. so you probably get to use maybe 500-1000ml of beer that otherwise you (or i at least) would leave behind.
beer loss in the filter - less than 250ml. Two ways to recover almost all of it.
Note - my filter and keg are completely filled with CO2, i dont purge, i have a keg filled with sanitiser and i push the sanitiser out of the keg, through the filter with C02 - so the air is fully displaced. purging isn't effective enough for me and C02 "blankets" are the product of over active imaginations.
The first stuff that comes out of the filter is fine and oxygen free, goes to keg - no waste.
Option 1 - If you need all the beer in there to fill your keg - At the end, when your fermenter is empty, before any air gets in the line, detach the tube from the fermenter and hook it up to a C02 source, push the last beer out of the filter with C02. Lose only a couple of hundred ml tops.
Option 2 - If you have a little spare volume - just turn the filter upside down and let it drain by gravity.... which will bubble air through the beer, mixing oxygen, so you dont want that in your keg. I put it into a PET bottle, where you can
a} bung in a spoon of sugar, naturally carbonate it and see for yourself, every batch you make, whether the "alive and natuarlly carbonated is better" argument holds up
b} screw on a carbonator cap, whack some gas onto that puppy, shake the **** out of it and reward yourself for your efforts with a virtually instant sample of your brew. or at least drink it first before the oxygen can do its evil work.
So for me, filtering wastes only about 200-250ml and gives me a net result of probably a litre or so of extra drinkable beer per batch vs finings/cc. I suspect that if i fined all the time i could refine the process and make it comparably efficient to filtering.... but i dont see that i could make it better without being willing to drink some cloudy beer.