Witzend, I haven't had milk in my tea for many years now, and if I do try it with milk it tastes greasy to me. So if that's weird at least you're not weird on your own.
I do disagree about leaf tea in a pot though. It's really a matter of knowing how much and for how long. I do pride myself on my precision tea-making! There was a myth once about "one spoon for each person and one for the pot", which makes the tea far to strong for me; two spoons only for my two-mug glass teapot (with strainer in the lid). That's a reminder that you should use the right-sized teapot – don't half-fill a big pot for all sorts of reasons. Also the water shouldn't be boiling but just on the point of boiling. That extra degree or two is critical, actually boiling water brings out the tannins that make the tea bitter. And for a small-leafed black tea three minutes to brew [mash, steep] should be plenty. After that I pour my tea and put the rest into a travel mug so it keeps hot without sitting on the leaves.
For me, loose-leaf tea will always be better than tea bags, which I have long suspected of harbouring the dust, twigs and mouse-droppings swept from the warehouse floor. Never trust what you can't see!