my iphone

How to erase your iPhone, iPad, or iPod touch - Apple Support

Erase a device in Find My iPhone on iCloud.com - https://support.apple.com/guide/icloud/erase-your-device-mmfc0ef36f/icloud - "If your iOS device, Apple Watch, or Mac is lost or stolen, you can erase it if you set up Find My iPhone on the device before it was lost." "When you remotely erase a device, Activation Lock remains on to protect it. "

I would think the above would also work over cellular since all it needs to do is receive an "erase data" message.

Yes, you can. If you want to delete the whole phone you can do it here:

Settings -> General -> Reset -> Delete all content and delete all settings

NOTE: This WILL erase everything and restore the phone to factory settings.

Remember to sign out of Find My iPhone and sign out of your Apple ID