Yes. Actually there are even new AVRs from SONY and Yamaha at that price range. rated at 100W and 80W respectively. Yamaha has Optical input while SONY only has RCA in.
But wouldn't it be a bit big in size. For Desktop usage.
Most "bookshelf" speakers don't get used on actual bookshelves. The idea that a "desktop" system need fit on a desktop is perhaps it's most limiting requirement. I have my desk off the wall and have my AVR and subwoofer amp between the front of my desk and the wall. Only time I have to get to it is to dust so I just pull the desk out occasionally. I use either floor standing, or stand mount speakers on either side of the desk. Only audio equipment on my desktop is a tiny USB CD transport.
The AVR I have is a pre-HDMI Denon 3805. It's rated at 120 WPC into 8 ohms. I never worry with what I want to hook up to it.
$200 is a silly budget, really. I work a full time job. With some patience and perseverance, I can reliably and comfortably save $1k/month. It means I have to cook my own meals and brew my own coffee, which I prefer to do anyway.
I am considering a pair of the new JBL L100 Classics for no other reason than I like them. The 4-5 months it would take to get them goes by in no time. I'm actually close to it now. Whether I pull the trigger or not is another matter.
Fk the financial institutions budget limits. Save the old-fashioned way and cut them out of it like the cancer that they are.