Not true. Companies hire recruiters to find employees. Not all companies (especially startups) have their own internal recruiting department.
The flip side is true, though: as a company trying to hire people, every recruiter email that says "I have a perfect candidate for you" is junk. They just invent those people or send resumes of people who aren't even on the job market.
A founder should personally be handling recruiting until the company is big enough to have their own internal recruiting department.
This is false. My last two roles were both initiated by 3rd-party recruiters.
If you don't have any way for companies to target you themselves, then 3rd party recruiters might be more effective the you targeting companies directly yourself.
However, if you are in the boat where you are getting many recruiter emails a week, my advice is sound. They are all junk, and the only way to get any signal to noise is to look for ones directly from the company doing the hiring.
They have their own recruiting team that you are going to be dealing with anyway, and aren't playing the numbers game or shuffling their candidates between many different companies trying to get their (usually very large) hire bonus. They just throw as many people they can at as many companies they can till they get a bite.
Senior employees can be up to a FULL YEAR of the hired employees salary. As that employee you don't pay it, but it's not something that is benefiting you either. On top of that, the companies often have claw backs. If the employee leaves under a certain time, they have to give back their fee.
The reason they don't respond after the first email, is that they need someone who is going to be very proactive and actually motivated to get hired. Else their candidate catapult might hit the target, but less likely to stick.