Dish soap on hair is actually awful, leaves it dry, clumped/stuck together, and unmanageable. I got something in my hair when I was under 10, all I remember is it was SO BAD I willingly went to wash my hair.

I have a similar routine to you I don't blow dry either it is towel dry, except I condition each time I wash, and get the same responses from women who equally do not like the "I wash, condition, and cut it (well its been a few years now but) every 3 months, and do nothing else."