I don't know a single venture capital investor who doesn't get a firehose of e-mail. You have money, they have ideas, so BAM, e-mails. It's just the nature of the job.
You could try and hide your e-mail, make people jump through hoops to get it, but at some point, everyone's got it again.
Even if not, by making it difficult to contact you, except through trusted introductions, you're implicitly saying "I think my next best deal is going to come from in my circle, as opposed to from outside of it."
That unfortunately reinforces the lack of diversity in venture capital circles these days--unless you happen to be that one white male venture investor whose tech friends and connections aren't also mostly white males.
Maybe if you are a Series A investor, you can get away with only taking inbound through intros. Most of the deals you fund have already been funded by someone else, so you're most likely going to see a deal through a seed investor you probably know.
But if you're a seed or angel investor, putting in someone's first capital, I don't think the warm intro criteria solves any quality problems, and it just creates a lot of work for everyone involved.
First, the entrepreneur has to go find someone who knows me. Since I've been in venture capital and tech for almost 15 years now, that's not really that difficult. However, since LinkedIn treats everyone the same, regardless of strength of connection, you'll likely wind up asking for an intro from someone really really random--someone who I generally wouldn't trust to vet my deals for me anyway.
Of course, they don't know that.
In fact, there's maybe five or ten people on the face of the earth I'd take a blind intro from. Everyone else doesn't really increase my interest in a deal. They're not VCs. Why would they be any good at spotting good opportunities?
Ok, so that person asks me if an intro is ok. I finally get a moment of focus for this opportunity and I'm faced with two choices:
a) If I like the deal, I ok the intro, but now I have to watch for yet another e-mail, when all I want to do is connect to that person directly.
b) If I don't like the deal, and this is the part I hate, I make the person introing become the messenger--that my time is too valuable for me to even want to e-mail with the person. That makes the person in the middle look bad, that they couldn't get their friend in the door, and it me looks like a pompous ass, because who the heck am I that my time is so important that I can't even e-mail with you?
What I'd much rather have is the following:
You just e-mail me, and reference who you might know who may be able to vouch for you. If we don't know anyone in common, that's alright.
Or, if you really want to get someone to intro you, fine, but have them make the direct intro, copying you. Know that I won't necessarily take the meeting, but at least you and I can be in a direct dialogue so that I can tell you why I might not be interested.
No VC has a magical stream of only high quality deal flow. I know this because I used to vet VCs for a living and they all pitch to their Limited Partners how many deals they see and how few they do. Screening is part of the job.
Plus, direct screening can be useful to a VC's future deal flow. The more people I give decent feedback to, or to whom I indicate what I'm looking for, the more people who leave off with a favorable impression of me. Given how networked entrepreneurs are, that means they'll tell others to pitch, because it was worthwhile even though they got turned down. Maybe they'll remember it for their next company. That's all positive word of mouth marketing that I need if I'm going to continue to see opportunities early.
So don't bother my friends for an ask. If you're in the NYC area, have yet to raise $750k in a previous round, just e-mail me.