Of course, the success rate won't be zero and you are bound to get your foot into the door in some companies but set expectation should be of getting a cold shoulder many many times.
The success rate, however, can be tweaked by —
a) Being a bit influential (like, having many Twitter followers or a somewhat famous blog)
b) Establishing a context. (hey, I read your piece about the SPECIFIC PROBLEM and that's something we're working on).
c) Writing something that puts you way above the crowd. (my friend often used to read people's Twitter and LinkedIn profiled before requesting anything. Like, "Hey. I read how you recently paid off your education loan. Mine is still pain in the ass")
I understand that if the problem is super-relevant to the business, they might agree in a whim but usually, it won't be the case. I am not undermining the value of the approach, but it's just not that simple as often portrayed.
This email looks great. Will try it out and tweak based on who I am getting feedback from. Thanks !!
See: Github, Slack
Cold email / LinkedIn should actually work fairly well for this. If it doesn't, your approach might not be specific enough, the person you're targeting might not be the right person OR your problem hypothesis is flawed.
Re: general approach, I've seen great response rates with a template like this one below.
Hi <NAME>
It looks like you’re an expert on <SPECIFIC FIELD YOU’RE SOLVING A PROBLEM FOR> - I would love to get your opinion on something I’ve been working on.
<ONE SENTENCE TEASER>
I’m not looking to sell anything at this point, but would love to understand if something like this would actually help you with your job. I don’t want to build the wrong thing!
Would you be willing to hop on a brief call with me sometime in the next week? This would only take a few minutes and if we’re onto something, you’d be the first to know about it.
Best, X