Yes HA < > Homey is completely local.
I wrote about latency: it’s quicker! Depends on the wifi setup and interference of course.
You don’t need to, but both have their (dis)advantages.
I started with Homey, and wanted to explore H.A. later on.
I still prefer advanced flows to automate, and use H.A. for zigbee (z2m is heaven compared to Homey zigbee), Matter (not available@ pro 2019), and for Homey unsupported devices, and to be able to use more apps/integrations (a Pro 2019 has 1GB RAM) > HA is only limited by the host’s storage and RAM (but SHS now has only the host limits as well).
And not to forget, I’ve built (WEB)dashboards to my likings a few years ago. With MQTT any Homey device can be synced with HA.
I can’t and I won’t choose for now 
