Is leaving NFC on a privacy risk?
Not in the way the question implies. An enabled NFC radio does not broadcast an identifier and does not announce your presence to anything; it waits to be brought near something. The real exposure is that a tag you did not choose can prompt your phone to act, and that is a small, local thing.
The radio waits
An enabled NFC interface is not transmitting your identity to the world. It has nothing to transmit: there is no identifier associated with the phone at this layer.
A phone looking for tags does generate a field periodically, which another device close by could in principle detect as the presence of a polling device. That is presence, not identity. When a phone polls at all differs between platforms and screen states: Android documents that a device looks for tags when the screen is unlocked, and Core NFC is where the iOS behaviour is described.
Compare that with technologies that advertise continuously with an address attached, which is a genuinely different situation and the source of most of the anxiety transferred onto NFC.
So the honest answer to the question as asked is no, and the interesting part is what replaces it.
The exposure that exists
A tag somebody placed can prompt your phone to do something when you put the phone down near it. The prompt requires a couple of centimetres and it requires you to be there.
On an iPhone this surfaces as a notification asking whether to open something, and a web link does the same on Android from Android 17, as the Android NFC basics guide describes. Earlier Android versions open the link directly, without asking.
What that gets somebody is a chance to show you an address. It is closer to a sticker on a table than to a compromise of the device.
The scenario where it matters is a place with tags you did not put there, and the answer there is to look before following, not to disable a radio.
Compared with what
The location services on the same phone, which are permitted to know where it is continuously, and which most people leave enabled without a second thought.
The applications on it, which have accounts and connections and are the actual route by which information about a person leaves a phone.
Against those, an interface that does nothing until an object is two centimetres away is not where the privacy budget should go.
Attention is finite, and spending it here means not spending it where the collection actually happens.
If you want it off anyway
That is a legitimate preference and it costs little: you lose tap to pay, tag reading and any routine you have built.
Both platforms allow it, and the mechanics of turning it off, including partial measures on the reading side, are covered on the smartphone side of the site.
Battery is not a good reason, and anybody offering it as one has not measured.
The better habit, if unfamiliar tags are the worry, is to read them with a tool rather than let the phone act on them.
Frequently asked questions
Does an enabled NFC radio broadcast my identity?
No. There is no identifier at that layer for it to send. It waits to be brought near something.
Can somebody detect that my phone is nearby?
A polling device generates a field another device close by could detect as presence. That is presence, not identity.
What is the real exposure then?
A tag you did not choose can prompt your phone to open something, from a couple of centimetres, while you are standing there.
Should I turn NFC off?
Only if you prefer to. It is a legitimate preference that costs you payment, tag reading and any routine you built.