In about 1991-1992 roughly, Campagnolo and Shimano came out with the shift lever/brake lever systems we use today. Pros were the first to use them of course. But the rest of the bicycle world picked them up fairly quickly. The clipless pedal came on the scene a couple years before Ergo/STI. Clipless pedals were also picked up by the rest of the cycling world pretty quickly. I used clipless Time road pedals on a loaded tour of Europe in 1992. Used bar end shifters back then. Anyway, downtube shifters died out pretty quickly after the advent of Ergo/STI in the early 1990s. It still existed but many or most new bikes sold, especially more expensive ones, had the Ergo/STI shifters. Bike equipment makers are in business to make money. If they invent a new way to do something, they want to sell it to everyone and make profits. Staying with the old ways does not help them.
Are people still using downtube shifters? Not really. Every now and then you may see a bicyclist using them. But he will probably be over 60 years old riding a bike that is 40 years old and has nostalgia for the past. Its kind of like asking if someone drives a manually shifting car. About 10-15-20 years ago they were sort of common. But now days you have to specially order a manual transmission car. Go to a car lot and ask to see a manual Honda Civic or Toyota Corolla, two small, efficient, light cars that usually had manuals a long time ago. Not sure you will find any on lots now.
A detriment to downtube shifters is they were almost always friction. You manually moved the levers so far to shift either the front or rear. You had to know how much to move the lever for each shift. Feeling your way. Or get scraping and rattling of the gears. Click shifting, indexed, downtube shifters were only around for a couple years before the advent of Ergo/STI brake-shift levers. Click shifting on downtube shifters was fairly good. You just moved the lever until you heard or felt the click. Perfect shifting, sort of. And in downtube shifter heyday, there were only 5 cogs on the freewheel on a 120mm spaced rear hub. Easier to manually friction shift when there are only 5 cogs. Big and little are easy to find since you just move the lever all the way forward or back. It was just the middle three cogs you had to "find" with the lever. Somewhat easy. When you get 6 or 7 or 8 or 9 cogs then its even harder to find each cog manually.
Unless you want to build a retro, old style bike and relive the glory years of Eddy Merckx, its best to avoid them. Or maybe if you want to salvage parts from bikes you find real cheap at yard sales and live in a flat part of the world. Downtube shifters work OK if you rarely shift your bike. I frequently go on 50-60 mile rides and might shift 5 times total. Downtube shifters would work well for me. I also ride a single speed bike on those same rides and never shift at all. I might choose single speed over downtube.
I also think the old time racing bikes of the 50s-60s-70s look good with downtube shifters. Better looking than almost all the current bikes. But not better functioning. The only bikes you will see with them are extremely cheap or extremely old bikes.