Imagine if those sites had to build their own captcha service instead. How much more expensive would they be?
Labels can also be obfuscated with javascript, replacing the raw HTML "Email" with "Age"on page load. Getting this right will require the bot to parse both HTML and JS, and we can force them to handle CSS too. Add a "zip" field, and hide it with complex CSS rules. If it contains a zip code, it's a bot.
If you're really paranoid, randomise combinations of distinguishable fields (name, email, phone, age and hidden fields) every time you generate the form, so even if a bot herder manually maps names to fields one time, it'll fail the next. At this stage it'll be cheaper for the bot herder to use Mechanical Turk, after which even Google's captcha is compromised.
Accessibility is very important, and if accessibility features are implemented well they'll often be useful even to people without disabilities, but do any CS/SE or code bootcamp programs take the topic seriously? I'm sure it must be taught somewhere, but it doesn't seem to be common at all. Can you even imagine 21st century university architecture department that didn't cover ADA compliance? That'd be unthinkable.
I can easily imagine it: architecture departments from universities in other countries don't necessarily have to cover compliance with USA laws.
Or a blind user who might actually rely on both labels and names. That's a bit like what arxiv does, they have hidden links that ban your ip when you crawl, but the links aren't hidden for AT users. I got myself banned that way once.
maybe to save them a few $ from bots and spam (bandwidth and storage is very cheap today) they might be losing new users by the thousands (and traffic acquisition is far more expensive than the formers)
Recaptcha isn't obnoxious for fun, it's obnoxious because this is the state of the arms race right now. There's also the challenge of creating a captcha that allows blind people in.