I asked feedly about HTTPS support in their Android app. Here’s how they responded just now. Still somewhat disappointing that HTTPS is not available across the board (don’t use Feedly over public WiFi!), but not really unexpected.
“feedly Pro is only available on desktop for now. We are working on
bringing the pro features to all of the connected apps (mobile and
partner apps). You can expect to take advantage of the pro features
across all platforms shortly!”