I'm not sure how much the investment community uses LinkedIn, but it seems like the closest thing to a solution right now.
1) Comes across as impersonal to the person I'm contacting. 2) LinkedIn is often checked infrequently at best.
I'm sure any solution would have same obstacles to overcome, but this is why I don't use it.
I disagree. The "busy person" didn't ask to be put on the spot to decide whether the inviter's social capital is insufficient to overcome their busy-ness or lack of interest in the intro or whatever reason they have for declining, so you shouldn't put them in that spot.
Assuming it's laziness totally misses the social dynamics.
Consider the case of a friend looking for a job. If they come to me asking for an introduction, they may be open with me about things they wouldn't tell a stranger in the first minute of contact. E.g., concerns about the target company, fears they might not measure up, things going on in their life. It's hard for me to know what they don't want shared, I want to minimize the risk a violation of trust, and I don't want to guess at what the recipient might have an issue with. So I'll always write my own intro or ask for something I can forward.
Also, if someone dumps some unwelcome request from a pal in my lap, I'd be irritated that I had to do the work of bowing out. It's their friend, not mine, so it shouldn't be my problem. For that reason, I always ask permission to do an intro unless I have strong reason to believe the intro would be welcome. (E.g., if somebody told me they're looking for developers, I'll do intros without confirming an interest in each specific person.)
That board was not well-functioning.
Knowing what information (is appropriate) to share with whom is not only not dishonest, it respects other people's privacy, and is a key life skill for effectiveness.
Here's a simplified view of my email life: I have a couple hundred people (the intermediaries) I have worked with before or am friends with who each work with or talk to many entreprenuers. Each of these people knows dozens of investors. When they like an entrepreneur, they try to decide which investors would be interested in that entrepreneur. This isn't easy because angel investors change what types of things they are looking for and whether they are looking for anything at all all the time (based on what they have already invested in, on how much time and money they currently have to invest, etc.) They then send out intros to many investors. I get about a thousand of these a year.
Now, there are two types of intros. The most common is "[Founder] is looking for an investor for his company, which looks like [company]." The second is "[Founder] asked to be specifically introduced to you." If the latter, I always take the introduction. If the former I filter for only the stuff I might actually invest in. This saves me time because--since I have a pre-existing relationship with the intermediary--I can say something like "I don't invest in companies like [company], I am looking for [thesis] right now." This takes 30 seconds. If I was to reply to the founder, it would take a lot longer not to be rude. Rudeness is discouraging (I know, I raised money for my own company, lots of investors were rude), and it burns bridges. If an entrepreneur told an intermediary she thought I was rude in my reply, that intermediary may no longer send me anything. I know I, when I've been the intermediary, have stopped sending people stuff because the feedback from the entrepreneur was that they were rude.
Also, the whole point of the intermediary is to save the entrepreneur time. The intermediary sends out a score of emails asking who is interested, and some smaller number reply. The intermediary then makes the connection. Now the entrepreneur only has to deal with the people who have self-qualified as potentially interested. This saves them time (and also puts them in a slightly better negotiating position.)
The only negative to this process is the time it takes for the intermediary. I am an intermediary as much as, or more than, I am a recipient of these intros. It takes time. I've often thought about how to automate much of this introducing work: deciding which people would be most likely to want the intro, sending the emails, tracking replies, making the intros, and tracking which intros worked to feed back into the process. I suppose this is what software like Salesforce does for salespeople, but I've never found a personal CRM that can do this for me. Would love to have one.