How do I get my Father, who has been diagnosed with Alzheimer's, to take a shower?

There are bath aides available. They come to the house, you get everything ready for them ahead of time and they're in and out in about 1/2 hour. They'll assist your dad in the shower and even help him shave if he'd like that. I went through this with my dad who didn't want to shower and I felt like you did. As his daughter I didn't really want to get in there and help him myself and I'm sure he felt the same way. I talked to my dad's Dr. who ordered a bath aide to come over. She came a few times when my dad decided that he wanted to shower alone and we never had another issue with it.

The first thing that came to my mind was, "Well, Dad. What else do you have to do?" But that would probably be seen as a bit smart mouth.

Taking a bath is definitely not a waste of time. It helps to keep the skin healthy. It also helps to keep the odor down. An important thing in men is to keep the skin of their private parts clean. If the skin there gets raw from being unclean, then it will cause a lot of pain and unpleasantness.

Do you have a shower that he can get into easily and a shower chair? That is important, since many older people are afraid of falling, and rightly so. Bathrooms are a common place for falls. With my father, it helped not to give him an option. When it was bath time we warmed the house and got everything ready for him. My mother stayed in the bathroom with him while he showered. When he finished his shower, a nice warm towel was waiting for him. He always felt better after his bath, so it was a bit of reward for him. (But even then, he dreaded it the next time.)