I can't figure why anyone would want to download the whole database.
Like @drzraf said, for archival reasons. But also for data analysis. Even if it's a snapshot (through there are solutions for that, of course). For example, if you're doing research on how language evolves, subtitles are a great way to get dialog. In real life, I'm hearing more active gender-neutral language (using "they" and "their" instead of "he" and "his", or in Spanish, using "todes, amiges" instead of "amigos" or "amigos y amigas".
One might also want to research how race is is discussed -- "negro" used to be an acceptable term, then African-American, then "black" and now "Black" (capitalized when written).
These are just examples, but you asked why anyone would want it, and my answer is that subtitles represent dialog and is a rich source of data.