I believe the most important determining factor is the quality of the teabag to begin with. Most teabags are made from tea crumbs shed off during tea processing. Although I didn't try many of them, I assume they are bad. In recent year I've noticed some teabags made from the tea crumbs from final packing of good loose leaf, and they are pretty good. I've also noticed some good CTC black tea that could be good for making teabags, and also noticed a good teabag product from trader joe.
I guess my response is a bit off topic
Overall I don't believe we can do much to make bag teabags taste significantly better. But finding the few good teabag products in market may be easier than working on brewing parameters.