Alexa already uses the Internet.
Unless you're only using the Alexa for Windows app on a wired PC and not any of the echo devices or Alexa app on a smartphone, Alexa uses WiFi.
The only "home wiring" here is power and messaging protocols over powerlines is a horrible idea and wouldn't be any less secure than WiFi (electromagnetic emanations turning all your "home wiring" into a big broadcast antenna) and why I think it unlikely that such a product exists.
Using proper security practices for whatever hardware and software you choose is how you're going to be most secure (keep everything updated, use strong, unique passwords, configure settings properly, etc.)
Look at what you want to do and choose the best/preferred devices to do it (do you just want to toggle bulbs, dim them, have colors and themes, control fans, motion-sensing, etc.). WiFi, ZigBee, and Z-Wave Plus are protocols used for all of these, depending on the brand. You might already have a ZigBee hub if you have certain Amazon Echo devices. If you go WiFi, ensure you can handle enough 802.11n 2.4GHz traffic in all your areas since that's what they use.