Sure, maybe the IPO shares sell for lower with higher rates, which may mean a lower total return for the VC. But to what degree? So the VC get $9 billion instead of $10. It seems to me the only thing that would affect is future fund allocation.
You missed the "fiercely skewed" part. The VCs have to be participating to begin with. Even one of these deals can make or break a portfolio, so they have to cast a wide net -- but the capital reserve is drier now. This disproportionately (and negatively) impacts VC returns -- it's not the difference between $10 billion and $9 billion, it's the difference between $10 billion and $100 million.
Additionally, higher risk-free rates of return mean that investors demand results _today_. If the risk-free rate is ~0%, the market is content to wait; capital today is about as valuable as capital ten years from now. But if it's, say, 6%, then investors need bigger returns and sooner from your VC funds to beat the market at large. But the cost of building the company hasn't changed, so this makes VCs have a harder time.
I suspect you're overestimating the impact of bond rates on VC or IPOs. What does the data say? IPOs have declined during a period of low rates, and at first glance there doesn't appear to be any clear correlation between inflation-adjusted IPO size and interest rates. Know of data that says otherwise?
Even A16Z lists a bunch reasons IPOs are declining (in a period of low rates), none of which seem related to bond rates: https://a16z.com/2017/06/19/ipos/
That is the expected result. Firms can take longer to pay off because the cost of capital is lower, and VCs are under less pressure to deliver. What you'd want to see research on is IPO returns accrued to investors.
Andreessen has been raising massive funds (because they can since investors were flush due to low interest rates) which need to write large cheques.
They aren’t doing traditional venture capital as much as late-stage growth equity. Since no quality company will sell half of itself to Andreessen, this almost necessitates writing a big cheque into a multibillion-dollar round at $30bn valuations, or medium-sized cheques into terrible ones. The former go public at $10bn, the latter go bust.
How does it do really well? By having a very profitable in-demand public IPO.
How do you get macroeconomically favorable in-demand IPOs? Lots of capital looking for alternative returns.
What creates willingness to consider alternative returns? Among other things, reductions in the risk-free return rate obtained by bonds.
High bond rates reduce the demand for alternative returns, which reduces the demand for IPO participation, which in turn affects VC returns.