On the lack of equity purchases in the ECB QE plan

There's disappointment from some that the new ECB QE plan won't incorporate the purchase of equities.  A few points.

1.  Equities are issued by companies that can!  [Don't ever criticise this blog for lack of depth on finance matters].  And which don't need to go via banks.  So, if there are finite funds/risks to take on the public sector balance sheet, one could argue they should be concentrated on segments of the financial system that are most dysfunctional.

2.  On the other hand, even if there were no financial friction in the equity issuing sector, on second best grounds, it would be justifiable to buy them to offset a distortion somewhere else, especially if the purpose was to boost overall spending on the grounds that this were inefficiently low.

3.  Purchasing equities might stimulate firms at the margin who wouldn't normally issue, or not as much, to tap this source of finance.

4.  A question:  what's to stop member state governments tapping the extra demand for their bonds by 'over-funding', issuing more bonds than they need to cover a gap between G and T, and spending the proceeds on equities?  This would have a similar effect as the ECB doing it itself.  There would be no explicit risk sharing.  But maybe plenty of implicit risk sharing.  Some of the most strapped states would not be able to bear much more risk and such bond-financed purchases would be counter-productive for them. But some might.