Except for the difficulty of managing and keeping up to date with TLS (I'd have to upgrade my RPi's OS for example, to do it well), and the fact that it actually reduces performance for small simple sites with local readership, even with HTTP/2 for example.

http://www.earth.org.uk/note-on-carbon-cost-of-CDN.html

Edit: I note that I got downvoted, though no reply with reasons. I accept that it is currently widespread dogma/fashion that everything should be HTTPS, and there are some good reasons for it, but as someone that has worked in what might be called 'real' security in on-line finance for example, I fear that HTTPS-everywhere is as much security theatre or cargo cult as taking your belt off at the airport scanners...