There aren't many old movies (in the public domain) that are subtitled and/or have good audio... However, in the U.S., we have a huge amount of government audio/video that is captioned. Here's an example of using youtube-dl to download one of President Obama's speeches and extract the closed captions (which I believe are produced by the government) into its own VTT file:

https://asciinema.org/a/93ihv5er83mrpihh9i5m3s9o5

Congress has video for all of its sessions and it is transcribed. So does the Supreme Court (though not timestamped).