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Your choice. Some folks have issues with their router with it enabled. I have no issues with my ASUS, so I leave it enabled. With it on, it does end up leaving a trail of old connected mac addresses in my router's log history. If you run into a WiFi source that you have issues connecting to having it enabled could be the reason.
 
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If you typically use your iPhone on public networks (coffee shops, library, motel, etc), then the extra security with randomly changing your network address is probably a good thing - enable it.
If you do not often (or never) connect to public networks (and only use from home, or connected to your work wifi), then the "private address" may not be relevant to you.
It's a security "feature", but ultimately, the choice is up to you.
 
If you typically use your iPhone on public networks (coffee shops, library, motel, etc), then the extra security with randomly changing your network address is probably a good thing - enable it.
If you do not often (or never) connect to public networks (and only use from home, or connected to your work wifi), then the "private address" may not be relevant to you.
It's a security "feature", but ultimately, the choice is up to you.
Can it cause issues though? My router at home is the Apple airport extreme ac. I never manually enabled private address so is it enabled by default on iOS?
 
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.
 
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