I know you like to rely on loose theories that can be moulded to fit any scenario, but we can add some actual substance to your theory and see some of the flaws which lead to some misleading conclusions.
Cases fell from 25k a day in early November to 14k at the beginning of December, which is when the first set of rules were relaxed. There were plenty of Christmas shoppers and after shops re-opened they had jumped on up to 37k just a couple of weeks later. According to Google's
mobility data, you had almost as many people shopping in early December as you did in early September, when cases were 5x lower. By
some measures, retail footfall was down just a few % YoY. Clearly cases being almost 3x higher before Christmas amplifies the impact of the Christmas spread, and clearly the two sets of approaches in November and December led to different epidemiological outcomes. To say they both aren't working, with no distinction, is to ignore that obvious fact.
On top of that, the rules that were outlined at the beginning of December said people from multiple households could mix for multiple days over Christmas, which many people made plans for and stuck to. Many people in this thread said they were going to do exactly that, and the ONS survey released today suggests they were among millions. They made the very adult decision to do what was best for themselves, they bought the turkey after all, what's a bit of covid compared to throwing away a good turkey? So the cases flowed from the Christmas period, not Christmas day.
If you look at the dates the tests were conducted (rather than reported), you see a simple pattern. There were around 40k cases a day in the three days before Christmas eve, and 45k cases in the three days after Christmas day. It was growing each week as a result of people doing normal things like shopping, but it wasn't blowing up. On the 29th it jumps up to 81k, and on the 30th it was 71k. 5-6 days after Christmas eve and it goes through the roof. The only other day to go above 70k in the entire pandemic was on the 4th Jan, following on from New Year's, and they haven't finished reporting cases from that day. The 5th Jan already has 50k cases reported, and it might well join those days in the top 4 peak.
Suddenly locking down when things go out of control doesn't lead to a sudden fall. The surge in cases that came directly from Christmas and NYE mean there's much more of the virus in the community, and it doesn't all spread just at once. People that have it now pass it to people in their household a few days later. People pick it up with almost no symptoms, do shopping for the next week and pass it onto nobody, and then just one person gets it and they start another chain. Australia have had cases at almost 0 for months, but those small chains keep forming week after week, even when it's few people passing it on. Which is why when they had to lock things down in Melbourne, it eventually brought things under control but there was no plumetting.
So no, cases wouldn't drop like a stone imminently if the primary driver of this surge was Christmas and NYE. It just means the peak will be much higher, community transmission will remain much longer, and the health system might reach a breaking point it otherwise wouldn't if we continue to make these adult decisions. Likewise, the fact that lockdown isn't leading to plummeting cases isn't evidence that it doesn't work, because we know how it worked last time. We went from 500 cases to 5,000 cases in 3 weeks between March and April, and we went from 5,000 cases to 500 cases in the 3 months between April and July. The higher that peak, the longer it takes to come down. People don't get to have a couple of days where things are let loose, and then they can have a couple of days of living in isolation to make up for it. That isn't how community transmission works. That's the point. We assess that risk poorly as individuals.
Now that I've answered your question, can you answer the original question with a direct answer?
