The email is just a symptom of the actual problem - tracking. Rather than hit the report spam button, I'd recommend installing a browser add-on that limits tracking.
Reporting it as spam impacts their entire operation. Disabling tracking only helps yourself.
You're right. People should do both.
But does it? No matter how many times I click "Report Spam" Google is not going to wholesale block LinkedIn's E-mail operation. At least those E-mails will start showing up in my own spam folder, but that's hardly affecting "their entire operation".
This is like refraining from voting in an election because "my vote won't matter." If enough people "Report Spam" then even LinkedIn's email operation will start to be impacted.
LinkedIn may be a special case, and then Google may be a special case too. But it will definitely help for all the other countless sites that are not LinkedIn.