If so, that seems slightly odd that I'm going through my top 10 friends on linked-in, vouching for them so that they are now going to get some a cold email(s), but I have no insight if those 10 people are looking for jobs and want this email at all. I'm pretty much saying to my friends "Hey, I just gave your info to this random company so hopefully I'll make some money off you." (And yes, it is true that I'm "helping" them get a job, but the people I'd vouch for don't need help, in this market they can get a job very quickly)
I will admit that some aspects of what I mention above are true in the "screen-share call" example you gave above, BUT it's the fact that the screen-share alternative is clunky/painful which makes it more socially acceptable. The automation/scale of your new approach starts to feel more spammy.
When you say "No recruiter mails" on your website, what does that mean exactly? Who is the subject of that sentence and who is the object? Subject: weekday recruiter? in-house recruiters at tech companies? contingency recruiters? Object: me the voucher? the person I'm vouching for?
Note: I'm not trying to be mean or negative, I'm just trying to understand the full feedback loop, so I can be empathetic to all parties, especially my friends. :)