When decorating my kitchen table with place mats, I found out the hard way that if you use cloth mats they get dirt quickly and are almost impossible to clean, especially when you have little ones eating pasta and sauce. You might as well throw them out. I went over to my mother's house one day and saw that she had a clear plastic table cloth. I asked her where she had gotten it. She said the craft section at Walmart.
I use one all the time, but remember, if your table is wood, the plastic should not lay on it.
I have a wood top table so don't think that would work too well for me. I think having to wipe down that plastic would be just as much trouble as shaking out cloth placemats or throwing in the wash when they get too dirty. I did away with plastic placemats for the same reason....seemed more trouble to me to have to wipe off the placemats.
Am thinking you might be able to fashion an envelope out of the clear plastic (size of a small pillowcase) and slide the placemats into it (especially if you find the plastic hanging down and making your knees feel warm in the summer).
Then again, it might be a blessing in the winter time!
my table is wood and this works well just make sure that the table is completly dry before putting down the plastic