What you can do with email is move the problem to your most secure account or to an account that you know how to recover under essentially all circumstances.
As I mentioned before that it's just convenience. SMS based authentication is flawed and is also prone to SS7 Attacks but people just do it because it's simple. Nothing in the world is hack proof
I've been using the same headphones (Backbeat Fit) for the past year (purchase was based on Wirecutter's review http://thewirecutter.com/reviews/best-wireless-exercise-head...) and absolutely adore them. Solid eight hour battery, even a year after purchase.
I went the 'new keyboard' route when I needed to repair my Logitech K811 - I now have two keyboards on my desk, one for the mac, the other for the PC.. Absolutely ridiculous, but saved me wasting a day of installation (and inevitably having to re-pair the K811 in the future)
Doesn't the K811 have built-in functionality for changing it's bluetooth pairing by a button press? Does that fail to work or were you just disappointed in its build quality?
A confirmed email address is probably the easiest point of user authentication.
Other than that - I totally agree with you that giving an email address away for sign-ups is pretty icky, but a necessary ickiness as there's not much else to choose from except OAuth (Google/Facebook/Twitter/LinkedIn/etc)