In an ideal world, every inpatient needs to be staffed by an attending at some point. For serious issues they definitely do at some point, as posters have described above. Straightforward things, however, probably don't need direct attending supervision. As long as the residents are comfortable handling straightforward issue, I don't have a problem with it. From a billing standpoint, it's probably a better use of time to see clinic patients rather than go to the hospital and see patients - you can probably see anywhere from 2-4 patients with the time spent seeing one patient in the hospital (traveling, lining up timing while the patient isn't getting procedures/imaging done, etc.). The best situation is that somehow the patients can come down to the eye clinic if possible; makes it easier and care overall is better.
My opinion about the billing issue is that some consults are probably frivolous and are there just to cover bases medicolegally. It doesn't feel right to bill patients for non-urgent issues in the hospital because they already have a big bill coming to them anyway. IMO, let residents handle non-urgent things, and don't bill the patient for it.