The outer ear is involved in normal hearing, creating a variety of reflections and echos before sound stimulates the ear drum. I agree that without its involvement, headphones will sound less natural. Few headphones allow much involvment of the outer ear because they sit right on the outer ear surface, close to the auditory canal. However there are many circumaural phones, which leave space between the heapdphone driver and the outer ear and thus get at least some outer ear involvment in the listening process. Some that I have include the old Stax Sigma and the still available Koss E-9 electrostatic and an old Sennheisser 220.
Crossfeed will not increase soundstage, rather it will narrow it since it means adding some left signal to the right channel and vice-versa. You are effectively monauralizing the stereo signal. The channel separation will be reduced and the width or spread of auditory signal will be less. If you totally mix the signals you will end up with complete monaural sound, localized in the middle of your head.
The crossfeed supporters, and I am not one of them (I had such a system years ago and found it to be of no use except for a very few old recordings with much exaggerated stereo separation) seem to like it because it makes phones seem more like speakers. However speaker reproduction is not the ideal or directly comparable to normal listening of sound sources in space. Speakers create "phantom channels" because for example, the left ear hears the left speaker and then the right speaker, delayed by the extra time it takes the sound to reach the left ear. These delayed signals have no correspondance in real-world listening and are artifacts, messing up the sound. Headphone lsitening gives a truer representation of sound because its creates a situation more like your own head being present in a real soundfield. And that. is one of the reasons, most of us here are dedicated headphone supporters.
I also suspect that many users of crossfeed find that the particular cross-feed set-up they use, does some additional processing, changing frequency responses and the like, which work well with whatever phones they are using. Thus they are responding to some other aspect of the "crossfeed" than just the crossfeed.