Sediment (usually a build up of invisible dirt) is one thing, minerals are another but most times sediment doesn't cause any problems but people think it will. So they buy a disposable cartridge filter; and installing one is a nice project and makes ya feel as if ya accomplished something but.... That invisible dirt/sediment, it usually won't hurt a thing, so why filter it?
And if you have visible dirt, you need either a spin down or an automatic backwashed type filter or you go broke replacing disposable cartridges every few days. If you have a disposable cartridge type, remove the cartridge and see if that doesn't simply trap the visible dirt.
Usually washer hose screens are blocked by little balls of hardwater scale, not sediment. A "whole house" disposable cartridge filter won't do anything for that because the scale forms in the plumbing and water heater and hot water plumbing after the filter. If you have hardness scale problems, you need a correctly sized water softener.
HJ, I meant the disposable type filter.
Most people do not replace the cartridges when they need replacing, they replace them when they finally notice a reduction in the water flow (called low pressure by most...). But the main problem is that the 2.5" x 10" cardtirdge filter was never meant to be a POE filter. It was invented for POUse for like a soda machine, commercial dish/clothes washer etc.. The 4.5" x 10 or 20" has the flow rates and capacity to be a much better choice for POE but... they suffer the same replacement problems as the smaller one and cost mucho bucks and don't last that much longer on dirty water.