Others will/may disagree. And, some will say that their experience is different. But, I'm a big believer that sending emails, while it can't hurt and could maybe catch lightning in a bottle, isn't the best way to connect with a coach and get recruited.
There are coaches out there who say "I make it a point to open and read every email." But, in reality think about the volume of emails that must come their way.
My 2022 first started sending emails early in 2020. It was a researched and targeted list. A few got back to him. Most said fill out a prospect form. Some said we will send you camp information when the pandemic allows. Basic boilerplate copy and paste responses.
Kid committed in October 2020. Spoke to a lot of schools in the Spring and Summer of 2020. None of them were the result of those emails sent in early 2020. All of it was off someone speaking to the coach on his behalf and setting up a call or text exchange with the coach.
Big believer that you have to have a multi-faceted approach and exercise every avenue to try and get recruited. But, I do also believer that some routes have a greater probability of working than others - and networking, being endorsed by a trusted source, is one of the better methods. Unsolicited inquiries might work if you are lucky. But it's not favorable odds.