On macOS I got tired of dragging webvtt files onto TextEdit to view them, so I wrote a Quick Look plugin so you can just select the .vtt file and press the space bar to preview them.
You’ll need to download the WebVTT Quick Look plugin and install it in the ~/Library/QuickLook folder. To view the Library folder from the finder, select the Go menu in the menubar, and hold the Option key (⌥). Drag the uncompressed WebVTT Quick Look plugin file to QuickLook folder.
You can either restart your Mac, or use the Terminal and enter the command: qlmanage -r
Using the terminal command above means you don’t have to restart your Mac.
Here’s where I got the information to write this plugin: Creating a Quick Look plugin.