The likelihood principle actually supports the Bayesian perspective on these issues of experiment design, and is regarded as foundational by many frequentists.
Agreed. But as Cox and Hinkley discuss, the likelihood principle is sometimes at odds with the repeated sampling principle, so in any particular application, you need to identify if there is a conflict, and if so, which principle is more important. In my domain (simple A/B tests), you can claw the repeated sampling principle from my cold, dead hands.