A lot of sediment is a mixture of rust from iron blocks, heads and pump rotors, and limescale from the water. When I replace the coolant on my engines, I use a 50/50 mix of antifreeze (which has rust and scale inhibitors) and clean water from the drain tray of my clothes tumble drier (it's not a vented one), which means that the water has been evaporated off and crudely distilled, leaving dissolved salts and minerals behind. I haven't cut any radiators in half yet, but peering through their top caps/plugs shows that they're still clean inside. I also back flush the system with a water mains hose at full blast whenever the rad or water pump are removed to clear out any debris.
I'm sure I still get some rubbish in the system, but by doing these things, the amount is minimised and the potential for rust or scale deposit and flaking are almost eliminated. This avoids the need for filters, which could easily become a blockage or leak point.