That's almost the point. Tennis has really got into the Olympic way of things - helped enormously that the Men's Big 3/4 of the Golden Era and te Williams sisters were heavily personally invested in it., but Golf relally hasn't had that moment - Tiger Woods was pretty much done before it even began, and Rory McIlroy was, like many others, pretty lukewarm. That attitude seems to be slowly changing, but the feeling remains gold at the Olympics needs a little gimmickry, something to make it different from just another tournament, but the powers that be are adamant the individual event should be a standard 72 hole strokeplay.
The team event allows much more format fiddling, and importantly a) can being the men and women together, which matters to the IOC and b) can show off the other major format, a very popular one - Matchplay.
My suggestion, with the goal to keep the event within 72 holes total, and simple enough for non golf people to get.
16 teams of 4 (2 men, 2 women)
4 groups of 4
Playing short round-robin 9 holes matchplay in the format :
men's singles x 1
women's singles x 1 ,
mixed foursome/alternate shot x 1
2 points a hole, 1 each for a tied hole, first to 10 pts(in effect 5 holes) wins - just a more causal viewer friendly way of describing the existing system (so 2 and 1 = 2 up with 1 hole left = 2 up after 8 = 5 holes to 3 (or 4 and 2 halves to 2 and 2 halves, etc)
If its 9-9 after 9, tie break is ruthless, one stroke 'nearest the pin' on 10th hole. to win single bonus point to win 10-9
Scores also act like goal difference to break ties, matches are best of three rubbers (obviously)
So thats 9+9+9, 27 holes to get to knockouts first round where 3rds play 2nds, again 9 holes ->36 holes
Day three the group winners meet the winners of 3rds v 2nds, again over 9 holes, then 4 QF winners play 9-hole semis
That's 54 holes
The medal matches are over 18 holes on the final day, but same rules except the winning mark is now 19 not 10. Otherwise, same format. Bronze medal match (consisting of 3 rubbers) goes ahead of gold medal match (consisting of three rubbers)
That's 72 holes - no longer than a standard tournament - if you want to make it even shorter ditch the group games, simply add scores from individual to create a team score, and top 8 teams go straight to QF round (wee bit like archery), whereafter system is same, that's just 36 holes over two days - Day 1 QF, SF both over 9 holes, day two medal matches over 18...