You can't 'spread it around' without taxing more.

Well let's tax more then.

VC/PE is cheap: it is money on which taxes have already been paid and if it does not work then it's their loss, not society's loss.

Society has already lost that money when the income wasn't taxed as heavily as it could have been.

Given the choice I'd take VC or PE based capital over a government backed fund.

If we spread money about through some kind of basic income then it wouldn't be government funds, it would be crowdfunding and community lending schemes.