I agree about how aligning the incentives can make a huge difference. The first product I was ever a product manager (and SME) for, I assisted the support team with escalations. This meant that every weird new bug or strange situation would hit me the same day. This really shortened the feedback loop on getting stuff fixed. It also made it so that I became aware of quirks or things that weren't working quite right from the customer's perspective, which is gold for a PM. That information I learned doing support escalations helped in the design of version 2 of the product, which is still in production 22 years later.

I strongly recommend having the PM be the highest point of escalation in the support chain. It really incentives them to make a quality product.