The word "modern" in the phrase is dumb -- as usual with the word modern; it's on of those word that convey no real meaning most of the times. It's not about modern, it's about power.

Current 32bits SoCs prolly sale for the same price as 16bits systems of a decade ago, so yes, they probably can handle HTTP. However, 8 and 16 bits microcontrollers with only a few kb of RAM/Flash are still made ("modernly"), sold and used - and those cannot handle HTTPS.