We did for years, and even have a pretty cool one with dual filtration that prevented almost all grit. (the Espro) However, I didn't enjoy the wasted coffee and cleanup, and found that using refillable pods used less coffee and mess for the same product.
The annoying cleanup and wasted coffee seems specific to the espro.
Cleaning a normal one is really quick and I don't mind the remainder of fines as they quickly settle at the bottom of the cup.
I filter my tap water because the water where I live tastes like mud sometimes. (No, I'm not making that up. And yeah, they've been working on it.)
I use an inexpensive carbon block filter that sits on my countertop and connects to the faucet with a little diverter valve. It works OK at reducing the taste issue here.
But I'm in no way under the impression that doing so somehow reduces the water's exposure to plastics. The pipes in the house are plastic. The pipes under the street, if recent, are plastic. The filters themselves are plastic.
I could get fancy and put in a nice reverse osmosis system, but that's just layers of differently-shaped plastic.
For me, the solution is to simply not worry about the things I cannot change.
(Although I guess I could go off the deep end and built a still... But sheesh.)
Eh? It's a carbon filter wrapped in plastic mesh, and the carbon part itself is a block that is bound together with plastics. :)
But if you want one, it is an iSpring CKC1C. Sets up quick, takes generic/COTS replacement filters.
(I used to use a Pur filter on the faucet and that also worked well, but it was filtering a lot of stuff that isn't an issue with my tap water, and the razor blade business model of vendor lock-in was more expensive to support than I preferred.)
It works surprisingly well, the coffee tastes better and it is not messy.