We run everyone through the shower every morning and have since my kids were very young - as infants my husband would hold each in the shower, wash them, then hand them out to me. As they got older, the oldest in the shower would help wash the younger one, then as the older child would get out, I would get in to give a final scrub to the younger.
Now baths are treats - not really something to get clean and showers are just part of our morning routine. That said, with a removable shower head, I believe that washing and rinsing are much easier that way because you can work the water down their hair. My daughter is 7, but I use my shampoo and conditioner on her and we have no problems with tangles - it's about shoulder length now, but even when it was mid-back this worked well.
Now...here's how my mom handled tangles when I was a child...I wanted my hair long. If I wanted to keep it long, I had to allow her to get the tangles out. If I fought it, no more long hair - period...and she meant it! I wound up with a pixie cut once - and NEVER complained again.