I disagree that the answers to the recycling/landfill issues is more wealth redistribution.
You are eroding your case to use these as straws. 
Whenever a shipment arrives, like from Amazon, I save the plastic airbags used to cushion the item. In my garage I have a large trash bag and I put them in there. I have a separate bag for styrofoam peanuts. I reuse them whenever I ship something out.
The large trash bags? They’re plastic, of course. 
Hee, you may not want to think too hard about the culture of mushrooms. 
If we can turn ashes back into wood, we can spare our forests. But reversing entropy to that degree takes godlike powers.
Or at least truly gawdawful amounts of energy.
If we can come up with free (enough) energy, all other aspects of chemical entropy reversal get a LOT easier.
I might have some bad-ish news for you.
How is an article about micro particles of plastic relevant to whether i use paper or cotton napkins?
It is extremely difficult to find textiles that have no synthetic fibers in them. Perhaps you are among the tiny minority of people who have. Or perhaps your laundry effluent goes into a septic tank. But microplastics from laundry are very much not a small issue. I believe I heard/read that most of the microplastic pollution in the oceans is from laundry effluent. So, you may be golden, but most people going that route are probably not.
? It is not in fact difficult to find clothing and household linens—and of course fabrics, for the textile DIYers—that are 100% cotton, or wool, or hemp, or otherwise devoid of petroleum-derived fibers that shed microplastics.
It is of course extremely difficult to find a large selection of cheap textiles at chain stores and the like that meet those criteria. No argument about that.
But ISTM that if puzzlegal is using 100% cotton napkins—which really aren’t that tough to find—then their laundering isn’t contributing directly to the microplastics problem. What else may be going on in her washing machine I can’t undertake to say.
I’m not claiming my laundry is pure as the beaten snow. But napkins, like towels, are really better when they are all natural fibers – those are much more absorbent than cotton-poly. We used to get linen napkins, but those are hard to find, and always look wrinkled. All-cotton napkins are easy to find, in fact, I thought they were the norm. Honestly, I’d be surprised if anyone is regularly using (actually using, as napkins, not just decorating the table) cloth napkins that aren’t natural fibers.
Well, then you need to be using new and improved BeatenSnow 
laundry detergent! Kills only half as many fish as other leading brands!
My new wife would have a word with you. Cloth napkins are always use-once-wash-once. Emily Post Said it, She Beleives it, and that Settles it.
Dishtowels too. [Where’s the sigh smiley when you need it?]
In burning wood, you are removing the energy that is stored in it. That’s not the same as with making plastic.
It doesn’t take a god even for turning ash back into wood, all that takes is a tree.
But for plastic, there are other options:
Now, I will admit that these are not commercial scale applications yet, and it’s hard to say how it will fit in economically, but the physics works just fine.
I was aware of these technologies when I made my statement, so my “if we can” was not a question of whether it was physically possible, but if it is something that we are willing to do.
Yes for sure. Other options are making component chemicals for other processes. E.g., lubricants, xylenes.
They all have supply chain and transport challenges. But the chemistry works.
If you come over for dinner, I promise you will be given freshly-laundered napkins. Just don’t look too closely at the napkins at the seats of those who live here and she’ll be fine.
I don’t wash the sheets every night, either.
I suspect Emily Post had a servant to do the laundry. 
Do NOT giver her ideas. Please!!!1!
I keed, I keed! but only some.
She is a most wonderful person who makes me very happy. But she comes with some rigid and to my eye silly-wasteful ideas about both cleanliness and etiquette. It’s an odd combination of aping the etiquette of the pretentious upper classes of 100+ years ago combined with cutting edge levels of dirt-o-phobia. But dirt-o-phobia in the name of etiquette and elegant style, not fear of germs as germs.
In this house we only wash cloth napkins once every week or two. Each individual napkin is only used once, though, we just have enough to last between washes. And do we ever have enough… Most of our napkins are reused material from worn out clothes, bed sheets, or whatever. Cut to size, sew around the edge, and napkin!
The cloth napkins go in a small laundry hamper in the kitchen (it’s an Ikea wire trash can). Kitchen towels also go in there. We go through lots of kitchen towels, but still only wash every week or two.
fwiw, my etiquette guide is Miss Manners, and she’s who told me that napkin rings are for the family, not for guests, and their purpose is to keep the napkins straight BECAUSE they aren’t washed every time.
You might want to introduce your wife to Miss Manners. Her original book is slightly out of date, of course, but is probably still the best. She’s funny, but very on-point and makes both a strong case for the importance of manners, and also gives some good overall guidelines for how to behave.
That was certainly my go to reference author and my attitude on cloth napkins in the Before Times.
In Certain Circles in my current home, Miss Manners is a dangerous radical preaching new and obviously apostate ideas.