Actually, I did speak to other Hams about your very suggestion because another Ham said the same thing, but I got mixed reactions. The one who used a bow and arrow actually had his wife do the shooting because she's an archer. Another said he tried this approach, lost a few arrows and was afraid he'd hurt somebody further away. And a few said they'd tried their kid's bow and arrow, removed the cups, but that they couldn't get very high with the arrow once they'd tied a string to it. One tried a monofilament line and that got over the branches, but said he kept breaking the line when pulling to untangle or to get the weight off further branches when it went too far.
When I looked at the price of an adult bow, they weren't cheap ($150 and up plus arrows) and a compound bow, which was the common recommendation, was even more expensive ($350 and up). The arborist's rope launcher was cheaper and could send up a weight with a 1/8 inch, 150 pound test line. So that was the product that looked like it would best meet my needs.
Also, I'm not sending a line over a lone tree, but rather over a tree in a tree line with many more trees in the forest behind - I'm at the edge of a forest. When I had tried to toss a weight with a line and couldn't reach the necessary height, it still often went over a lower branch and into trees behind it - it was not easy to pull the weight back down and I needed to sometimes pull quite hard. So I felt that light monofilament line really would break and I'd spend more time retying and re-shooting than achieving my goal. The arborist's rope launcher can send a much stronger line up and let me pull it back when I miss. Similarly, it'd also help me pull down a stuck drone or that of my friends who also fly.