You need to think this through more carefully.
First of all, Ft. Worth freezes every winter and some winters it gets really cold at night. Just last night it was below 15F. So, if you were to install your imaginary system it would have frozen solid and been destroyed (water expands when it freezes and it will rupture every single cannister, fitting, line and valve in the system when it does this).
Secondly, what do you mean by "filtration"? Are you just talking carbon filtration to remove a little sediment, large-scale microbial filtration, osmotic water purification? There is a wide range of levels of filtration depending on how small the objects are that you want to remove. Anything less than an osmotic purifier is pretty much useless because they will pass through all dissolved solids and most pathogens (like e. coli etc). If you just want to get rid of some rust/dirt, then carbon is correct, but if you want to purify the water to any degree you will need osmosis.
Thirdly any filter reduces the water flow a LOT and takes pressure down to about zero. So that means that if you want to, say, take a shower, you will have to repressurize the water after you filter it. So, the filter puts the water in a large tank, then you have to have a high-power pump that will repressurize the water coming out of that tank. For a typical home you will need a tank at least as big as a water heater, and even then you will run dry more often than you think. I would probably have AT LEAST one water-heater-sized tank FOR EVERY PERSON in the household. If you have a 4-person household, that is a big tank, 200 gallons or more.
Finally, your filtration system has to produce water faster than you use it. A typical family uses about 400 gallons per day. As osmotic system capable of producing 400 gallons per day costs about $10,000 to $25,000 and is the size of an SUV. Starting to get the picture?