As a middle aged person, my hair and scalp only need cleaned two or three times a week. Once I stopped believing the ads anyway, that aim for daily.
For a couple years, I did use home made soap (my skin likes it better than grocery store soap) without apparent damage to the hair. But. The hair was hard to keep neat. Also, we have hard water and there would be buildup on my hair and what looked and felt like soap scum on my brush. I have since switched to washing my hair with conditioner, avoiding those with sulfates.
IF I went back to regularly using soap on my long hair, I'd choose one that has lower cleansing effect (less stripping) and follow that with a vinegar rinse for smoothing and in hope of avoiding soap scum, and follow that with conditioner. For short hair I'd skip the conditioner.
If while away on short trips I've forgotten to bring conditioner, I wait until my hair must be washed and use the hotel bar soap once rather than hotel shampoo or conditioner, to avoid itchiness.
But that's my skin type, my hair type, my arid environment, and my hard water, without psoriasis or eczema.