FYI I've seen those gardeners kneeling pads at the dollar store sometimes. They are usually cut smaller than some of the nice big ones, but hey, for a dollar ...
My dog tracks in all kinds of dust and dirt, and he is not ashamed to show me his new sticker collection several times a day. Why dogs favor places full of stickers when the other 95% of an area is sticker-free, I'll never know.
I decided I like the warmth and softness of carpet, but not how hard it is to clean once you get it wet or really dirty ... the stains soak through to the padding and never really come out, even when repeatedly steam-cleaned. So I got some throw rugs, runners they call the narrow ones that come closest to fitting the narrow free passage my trailer has. I can take them outside and shake them out like cracking a whip. That always gets a rug much cleaner than even a really strong vacuum. I'd recommend that to people with allergy problems -- just wear a mask before you do the shaking?
My mother replaced the carpet in her living/dining area with artificial wood just a couple of months ago. She put throw rugs under some furniture. She gets massive amounts of dust and hair every day from her four dogs and vacuums every day with a hugely expensive vacuum cleaner.
About two months later, just to see what might have been left behind, I took her battery-powered leaf blower inside and blasted the throw rugs with it. Clouds of dust flew up high enough to settle thickly over door jambs, on the top of a ceiling fan, all over her shelves, etc. Big clean-up, but wow did that remove (eventually) a ton of dust.
So even if your carpet is new and you have a $400 vacuum cleaner that you use every day, yeah, your carpets will get full of dust really fast -- and keep it!