Samuel Suresh's YouTube video titled "How I Take Notes with My iPad Pro in Lectures" (https://www.youtube.com/watch?v=n0ql-yeY9u0) makes some pretty good points for taking handwritten notes on a device.
Akkshaya Varkhedi says in the article a couple downsides to handwriting notes on paper are:
1. Can't add screenshots, images, links, etc. 2. can't easily search for content.
Using something like Goodnotes addresses both of those items. You can take screenshots, add images, and links, and even use the devices camera to capture images (like the whiteboard/chalkboard during lecture). And (depending on how good your handwriting is), there is a search feature which searches the words you've written—and those words can be converted to type if you want to add them to a document without needing to re-type it.
Buying a tablet and stylus (like iPad and the Apple Pencil) to solve the two points paper notes does not solve seems a bit overkill—but in todays world, if you're a student going into University and need to purchase a device, those tablets are looking mighty attractive versus a standard laptop.