I have a problem with calcium/lime in my water that clogs the filter screen in my faucets. I have to clean them out about once a month. I just got a new Delta kitchen faucet (due to a remodel) which has a water restriction device that is supposed to conserve water. It seems most/all of the new faucets have this. Unfortunately, it seems to clog even faster and further down into the guts of the faucet and tubing(probably due to the narrow tubing). I had to have a plumber fix it.

Is this a problem that could/should be addressed by the water and sewer treatment plants? Shouldn't they take the calcium out of the water so this isn't a problem?

Best bet is to have a softener or filtration system installed in your home.