I use subtitles most of the time. It helps a lot with strange accents and noisy movies. I can watch most things without subs, but I have to turn up the volume and it can get annoying.
I've used some desktop apps that do the same thing your website does. It was really hit or miss and a lot of work. These days if I can't find matching subs, I either wait or watch without.
Instead of searching a dozen websites manually, I highly recommend SubtitleSeeker. It indexes all major subtitle sites and it lets you drill down by language, release, episode, etc.