That's the only way I have actually found and watched films over the course of the past decade.
I'll say, of the 320+ films I've watched over the course of the past 3 years, about 45-60% of them I watched completely blind, save for the knowing the title of the film.
I actually have made a habit of just scrolling through just film titles, and picking one that seems interesting, and pressing 'play'.
No posters, no quick synposis, no nothing. Sometime word-of-mouth helps, but when friends recommend me a film (I usualy badger them to) they just tell me the title of it, and I go on my merry way to locate it.
two notable examples:
From Dusk till Dawn and
Elephant
I watched both films completely without any idea of what to expect, who was starring, and actually the genre of film it falls into, and in conclusion, I found it thrilling afterwards to remember the experience of not knowing what to expect at all, and really enjoyed both viewings. I don't know if anyone would have had the same emotional reactions as I did watching these two particular films, and then wiling out, pondering where the direction of the story is going, and then coming to the realizaion that "film A" relates to "real-life scenario B".
Then again, my film-going is experience is not normal at all. I haven't been inside a cinema house since before Y2K, and I don't actively look to find "movie reviews" just to see if a film is worth it or not. I don't care all that much. Though, after just watching a film, I usually do hit up wikipedia or imdb a day after finishing it, and then start reading the plot and what the overall message and history to the film is, which usually prompts to watch the film again with some knowledge of what to look for, and what I might have missed.