Some users have issues with Private Address.
You would need to test with it on. If it causes issues with your router (which could be caused by interaction with whatever network that you use), then leave it off.
What issues would you look for? intermittent, or complete loss of connection, or perhaps problems connecting to sites that otherwise give you no problem. If you see those kinds of problems with private address on, then turn it off, try the same sites again, just to check that it is Private Address, and not something else.
Is it enabled by default? No one here can tell how your settings are configured. Check in your Settings/Wifi, and select your Wifi network, which will display how you have Private Address set for your network.
Finally:
Using a private address helps reduce tracking of your iPhone across different Wi-Fi networks
And, using that feature is entirely up to you.
If you never use Wi-Fi outside of your home, then leave it off, as it won't be particularly useful. If you often connect to
other Wi-Fi networks, then you might consider turning it on.
If you never turned it on, and you don't care to use it, then just verify that it is, in fact, turned off.