In practice most PM's have a VaR limit and a battery of dollar exposure limits, which are all set by the risk department.
There is some credible research which suggests that large financial institutions act as if they are optimizing mean return subject to a VaR constraint [1].
VaR is a fake number for way too many reasons to get into and anyone who paid attention to VaR these past few months would have lost a ridiculous amount of money. I only have experience working for hedge funds and how risk is managed greatly differs from fund/strategy/assets traded. Banks no doubt manage to VaR but banks also supposedly don't have prop trading desks anymore so they function much differently now.
The discussion seems to have shifted to argument for argument's sake.
But for the sake of argument: large bank VaR models affect hedge funds because hedge funds get their leverage through their prime brokers which are... large investment banks.
