YTA,

Be a parent to your child, and not a friend. You already know what the right course of action is. Your son will come to deeply regret that letter when his father is on his death bed. It is clear he has made mistakes in his life, but as you stated

But on paper his dad was a decent dad, always paid his support on time, never missed any of his scheduled time, and loved our son.

If he was a true deadbeat, he would have paid you nothing and left you and the child. Instead, its clear he was suffering financially and made promises he wanted to keep, but couldn't. Yes, that is a definite personality flaw,, but not worth burning a bridge with your father.

TLDR: Burning a bridge like that because dad didn't buy me a sports car is completely different than burning a bridge because dad didn't love, support, or acknowledge my existence.