Do this once, pax tells everyone about how they got into the lounge. Second time round, their friends are asking. 6 months later, some social media sharing and half the plane is asking for lounge access for a delayed flight.
If VA wanted to attempt this, a rule needs to be in place. ie delay of 300 Minutes or more for a child less than 5 years. Then you have the problem of a couple with a child 5 years and 1 day with a delay of 280 minutes abusing the staff. You will end up with bad publicity either way.
Looking at the big picture, you are better off just refusing, giving vouchers and offering apologies and sympathy.
I don't see how a 5hr delay with Taxi's and voucher is a "Saga"