but why pay hackers to try to find a backdoor when you can just walk in the front door and use the carrot and stick to get what you want?
Your question assumes two things: (1) That Apple intentionally leaves vulnerabilities in the stack, and (2) that Tim Apple is occasionally willing to share this candy with governments.
Having worked at Apple, I don't believe (1) can be true. Not only is it extremely unlikely that it could be kept a secret, but Apple's thing is "obsessive control", a mindset borne of organizational PTSD which originated with its near-death experience in the mid-to-late 90s. The Apple I know would not risk intentionally leaving back doors unlocked for enemies to find and leverage.
As for (2), the existence of a "Binder of Vulns" by nation-states would expose Apple to existential risk. It's possible that it could be kept secret within Apple's walls if it were never used, but once shared with a government it could not be contained. The splash damage of such a discovery could easily kill Apple.
Knowledge of a binder of vulnerabilities is perhaps one of the greatest secrets that must be protected. Wikileaks releasing the Vault 7 leak was the death knell of Julian Assange. It proved such a binder exists in great detail.
I don't hate Apple, but assuming they can't be reached, seems naïve.