Honestly, an internal employee referral helps in similar ways, especially from an employee who knows you well in a professional context. But that isn’t always available.
Even if only a few companies hire through direct contact, many of the ones that do will hire more than 1 in 10 of the relatively infrequent direct contacts, while their HR process may be sitting on the thousands of regular applications.
People should write you a cover letter on the off chance that you open a spam folder of such volume that you can't bother to manually label a mail as belonging in it?
If it's solely through LinkedIn fair enough I guess.
I’d suggest calling out on your job posting that LinkedIn messages may be missed and the email is the correct place to reach out.
Not to say that what you say will never work, but I think it’s worth pointing out that at some companies, application processes might exist for a reason. For me, having all applications in a single place is key to actually being able to deal with them effectively.