The Support Team knows the product better than anyone in the company which is extremely valuable if/when you get promoted to another position within the company.
I had some conversations recently where I offered my opinion.
"I think this might be a bit complex for the given users who are using this."
"But they want all this information, we're doing it."
A few weeks later end customers are all confused and they're up in arms because they can't figure out how things work because the product threw the kitchen sink at them on one or two pages...