Then maybe would be better to enlarge/increase the lounges instead?

I don't completely understand the bags on seats point. If there are no seats available for people then should be natural to ask for the bag to be moved, by direct or lounge staff request.
And I also would be ok for a "family voucher" one or two time a year. I'm not traveling that frequently, but during holidays, when I suppose the family travel is higher, I don't remember lounges so full you can't go in, nor discussion here about it.

On the other side, when I fly A* alone with the two kids of course I would like to be able to guest both, but since the rules say I cannot, well... I know I can't and that's it.
On OW no problem, they have lounge access by themselves, but I can't justify to double the flight price, in Y shorthaul moreover, just for being able to use a lounge all together.