I personally wouldn't have quit. I worked as an ED volunteer for 1.5 years and I cleaned rooms, made paper charts, did copies, run stuff to the labs. A lot of times there was not much for me to do however I worked hard and always asked if anyone needed help. That's what got me hired. My hard work ethic. Not being a volunteer.
The thing about following a nurse and watching patient care as a volunteer is HIPPA. Unless you are directly involved in the patients care volunteers really have no business being in the room. Nurses also do not have time to teach and stuff. Put yourself in the patients shoes. I would not want a volunteer in the room watching me or my nurse. Its uncomfortable and weird. I felt the same way as you at first but quickly learned its about the patient's privacy not about learning.
It was my hard work ethic doing work I did not want to that got me a job as an ED tech. I had no tech experience and would not have gotten the job without volunteering. I have worked at that hospital for a little over 3 years and the experience I got as a volunteer and especially as an ED tech I could not match with school or anything. I learned SO MUCH, got confidence, felt comfortable working with critically ill patients and codes and strengthened my skills and thinking.
Had I not been a volunteer I wouldn't be orientation this week for a level 1 surgical - trauma ICU nursing internship. I got a lot of bs as a volunteer and tech sometimes but it made me stronger. Everyone expects volunteers to be valued and cherished and nurses wanting to teach you. Doesn't work that way. Sometimes you have to work your way up the poll because the prize is at the end and I have my prize now doing what I love in my dream job.
There are always opportunities to get into volunteering in the future but do not expect a job offer to come because of it. Ive seen many volunteers and nursing students asking the charge nurse about getting hired as a tech. None of them did get hired because they were lazy when they were there and did not leave an impression on the staff. I had 3 references from the staff that got me hired as a tech. I wish you the best.