Actually you can -- on some airlines but apparently not QF. Sometimes time management is crucial to me and I pay very high fares and/or high status to get that benefit. LH HON mentioned above did that routinely, so did CX in its glory days (not so much now). I've made dozens of connections 5 min before departure time, and being the last pax to board, and could rely on this when scheduling my time and buying tickets. No longer true for QF (maybe an over-reaction, I remember when QF long-haul flights never left on time and they had to drag pax from the lounge to the plane 15 min after departure time -- very annoying). We keep hearing how 5% of pax make up 90% of airline profit, due to the huge fare differentials, but this won't work for QF if they keep doing what the OP described.
Bottom line, LAX staff acted for their convenience and not for the convenience of the pax. Which is fine if flying JQ discount economy, even ok for QF economy, but not when paying 10x as much for the same flight ... the differentiated service has to exist reliably, for airlines to thrive on this business model that they chose and control. Some other airlines seem to get this balance better than QF at the moment -- something Joyce has to fix urgently, imho, or he'll be eating humble pie next.