Exclusivity has so much practical value than the entire university system in the US is built around it. If you participate in a program that's considered to be exclusive, you will have an easier time standing out when competing in the future. It applies to people, and it applies to companies.
If YC isn't exclusive enough for you, I'm sure you can find a more exclusive accelerator.
In the eyes of customers, I don't think it would give you an "easier time standing out when competing", but I guess everyone is entitled to place their own bets.
Not in the eyes of customers, but in the eyes of future investors. I don't think customers should know or care what accelerator a company went through, although Cinder does advertise itself as "YC-backed" in order to convince customers that it's not a Kickstarter scam.