Not just a very British thing at all.
" having matching saucers sounds very aesthetic, but I don't entirely comprehend the pragmatic purpose of the saucer. Couldn't a coaster work just as well?"
—passalidae
"No" is the simple answer. A coaster can't hold a spoon and a couple of biscuits all the while being carefully carried one-handed out into the garden to enjoy the whole, whilst containing any spillage. Yes, a tea-tray would also work, and if needed can also bear milk jug and sugar bowl.
A cup and saucer is far more than an æsthetic choice, it's an incredibly pragmatic one. For years during my upbringing, a failure to place the cup on a sacuer would be met with "It's not a bloody picnic, you know!" from one of my parents. It's more that just elegance, it's about refinement and rightness. Walking two cups from kitchen to sitting room sans saucer means more than just the risk of a few drips on the carpet, it was a rejection of all that was British. The saucer completes the drink as cufflinks complete a shirt, in my father's eyes. Whilst i didn't always agree with him on everything, he had my complete support on this one. It still seems Just Plain Wrong to be served a cup without a saucer. a folded paper napkin can absorb minor spills yes, as a coaster can keep the spills from a carefully polished table. But it's more than that, it's a valuable tradition that says "I care". Not to mention a place to put the biscuit (by which i mean "cookie") once a bite has been taken. It works for tea, coffee, hot chocolate, and I suspect that the very Britishness of it was baked into all of us from an early age. Certainly I learned this at the same time I learned to make a pot of tea. The pot was an important component of the ritual, leaving me with the sense that as long as there was a good cup of tea with a saucer, All Would Be Well with the world. Do they have to match? No, but anyone who cares will buy cup and saucer as part of a set anyway.
My local cafe, pracically perfect in very other regard, fails in only this one. My coffee, no matter how excellent, for m still needs that saucer. For them, it's another thing to worry about, to break and replace. My pragmatic self understands this well, but my soul still aches.
I jest some, but for me this is part of the Good Old Days. My grandmother would no more neglect the saucer than she would leave the antimaccassar off the back of the armchairs. It's the very British attention to detail that helped make Britain an Empire (though the flag helped!), and unsaucered mugs part of the reason it failed.
https://imgur.com/gallery/tea-as-god-intended-ow7CDFr
$ xclip -o | wc -w
480