When we started travelling with our 4 tweens, it was a disaster. Anything that can go wrong, does, especially when there are 6 of you. Status means they generally bend over backwards to sort things out or spread that disaster onto someone else so you don't have to worry about it. My list:
1/ Lounges. Most business class lounges are pretty good and most F ones are great. We always arrive early to deal with the inevitable problems. Most of the time now, they don't even occur, so we just wander up to the lounge and relax. Try sitting in the airport for 3 hours with 4 kids. They will drive you insane and end up cost $200 in food. In the lounge, they just sit and play on their devices, eat the nice food and leave you alone. When you have a delay/cancel, its a godsend, or a nice shower/meal during a long stopover. Also, the counter in the lounge will take care of any problems you have far better than customer service dealing with the masses.
2/ Checkin. Normally a very long process for us. Straight up to the F counter and straight through to that lounge
3/ Choosing you seats (and those others have to pay for).
4/ Talking to someone in Australia, straight away, when you call.
Personally, I think status is great for the benefits when everything goes right, but the real power, is when everything goes wrong. That's when you are ever so glad you have it.