I believe keeping VPN connected drains the battery because some of the device's chips cannot "sleep"
A VPN-based app also disconnects when going from Wi-FI to cellular.
Worse, when going from cellular to WiFi (ie: going back home) with a VPN on, the iPhone just keeps using the mobile network until the VPN is disconnected
These apps usually try to auto-connect to VPN but when your connection is spotty, it becomes a very annoying, you have to kill the app, disconnect the vpn manually etc
As user you're left manually putting the VPN on/off constantly if you're on the move
It's definitively not a "set and forget thing". I wish Apple could give a way for ad-blockers and this kind of apps to function normally without using a VPN as a crutch