Spot on. The 'machine' only works if the profile layout does the heavy lifting before you even send a DM.
Most people treat their LinkedIn like a resume, but it needs to look like a landing page built strictly for your target audience. If your headline says 'I help X do Y,' but your featured section doesn’t prove it immediately with a case study or a breakdown of your system, your reply rate drops by half.
Optimize the profile asset first, and the appointments will follow so much easier.