It sounds as if you have a carbon blockl type cartridge. You can't get better, or higher flow through them because they adsorb and absorb things out of the water and that takes time. So find something else to do while filling large pots and enjoy very high quality drinking and cooking water.
What you're asking/wishing for doesn't work very well or at all. And it gets expensive buying cartridges so frequently. Plus that takes more time than filling a pot a few times a week.