I think you're going about this the wrong way... It shouldn't be about you, it should be about your client. What benefits them?
What's the purpose of them visiting a psychiatrist or psychotherapist? To get help. Would they feel more at ease with a therapist that feels "human"? Yes, but only up to a point.
The most difficult thing about talk therapy of any sort is getting your client to trust you enough to open up. Professional dress code help promote that image that the therapist knows what he/she is doing. It's the same with the "don't talk about yourself" rule. It's a little counter intuitive but sometimes objectivity gets people to open up more than when you're too up close and personal. The same deal with how people will tell somebody half way across the world very personal stuff online, but they'll never share it with anybody close to them. Keep it simple. The more disconnected they feel the therapist office is compared to "real world", the better for them to open up.