If your going to be in North America 99.9% of your time, its not necessary to carry your passport (but you should have one - never know when that last minute trip to Italy will strike your fancy!).
Personally, I carry mine. But I can be travelling the following day, or need info off my passport for any number of things. Yes, a photocopy of the passport would solve most of my problems other then the travelling, but a passport doesn't take up much room.
Chances are that if you don't have a need for it now, you probably don't have an every day need for it at all.
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"One should not increase, beyond what is necessary, the number of entities required to explain anything"
William of Ockham (1285-1349)