Matching private funding brings the decision making lever to private funders, creating a mechanism to extract tax dollars with minimal government discretion and would be a process ripe for abuse by those with significant capital.
One person's gatekeeping is another person's stewardship and due diligence
In comparison to just giving money today? Just look at the number of failed green projects in the EU where somehow the executives got rich and nothing got built or if built failed to deliver. At least with matching the private sector has to put a eur down for each it receives and the fund would own participations in ventures.
Another model would be for the EIB to commit money to an investment fund and then run a tender process to select a private sector firm to manage the fund. At the individual investment level, give that manager the usual discretion to invest and manage that VC funds have and pay them a market rate with an appropriate fee structure to do it.
You could also insist on the manager raising a certain minimum amount of matching private sector money to "keep them honest".
One person's gatekeeping is another person's stewardship and due diligence