Sorry, I feel like I've been really misunderstood here. I have no issue (and USE!) reminders for birthdays.
I do not have an issue with using reminders to help to acknowledge the birthdays of people I care about and who care about me. (Both close friends and more far-flung extended family). I would want to recognize and mark their birthdays, regardless of the way I remembered the date.
My point is all all all all about the random, almost strangers, (co workers from my first job 15 years ago, high school classmates, etc) who I've basically lost touch with. Well wishes, in my mind aren't about quantity, but about quality. A half-hearted "FB told me to write you, who are you again? Oh well Happy bday" is not in any way a quality greeting. Why bother? Now I look back at my timeline and I barely recognize the names of the people who wished me happy birthday last year.
They didn't do it because they care, they did it because there was a button to click.
ETA: I just thought of the right word to describe how I feel about birthday wishes from people who never talk to me except when FB tells them they should: its spam. Strangers spamming me on my birthday. How is that fun?
If you consider these people "random, almost strangers," "barely recognize the[ir] names," and consider well-wishes from them to be "spam," then why do you stay facebook friends with them?
A facebook friendship is not a permanent commitment, so if you're to the point that even a brief birthday wish is annoying to you, why not defriend them? If you are as out of touch with them as you say, they probably won't even notice!
The thing is, different people use facebook differently. If (general) you only want meaningful, "quality" contact with people who you're close to, that's great. OTOH, if you want to have huge, far-flung network of almost everyone you've ever met (and some you haven't), even if you only really make contact on birthdays, then that's great, too. But because everyone uses it in their own way, then really the only way to keep your own facebook account running the way you prefer is to manage your own settings and friends list.
Apparently, your "almost stranger" friends are fine with having distant acquaintances on their friends list. It's likely that they wish you a happy birthday because they enjoy having even distant "friends" do the same for them. However, you don't seem to like either of these things, so why leave the connection? All it does is allow them to unwittingly annoy you, which isn't what you want, and almost certainly isn't what they