I don't know about other guys, but my "morning wood" is not normally due to sexual arousal, but many times due to a need to urinate. However, I am one who does actually love having one of these erections. It may sound odd, but gives me an opportunity to play with, look at, inspect...my penis WITHOUT an overwhelming desire to either have sex or masturbate. I guess I can equate it to enjoying kissing your partner without the desire to "swap spit".

Don't get me wrong, there are mornings I am sexually aroused and the erection is purely a reaction to wanting sex with my wife.