Issue is due to the amount of spread, the issue is not large parties.
Even a group of 5-6 meeting at a house can now be an issue.
So, this is not correct for a few reasons.
1) At scale, Covid will be present roughly equally in the population. Meaning 1 out of every X people have Covid.
This isn't necessary true in every social group or neighbourhood, but it is when you consider behavior at a regional scale.
2) As such, the more people you invite to a gathering the greater likihood that someone, or multiple people will have Covid.
Yes, that could be true in a gathering of 2 random people, but is much less likely.
3) The larger the gathering, even if spacing or masking were otherwise observed, you're increasing the number of people likely to come into contact with the infected person.
4} The larger the gathering the less likihood that social distance is being or can be maintained, thus increasing the risk of transmission.
If you have a gathering of 4 friends at a home; there is an associated risk; but certainly, if you don't want to, you don't have to be in close proximity to one another.
If you have 40 friends/strangers over.........the odds are some of you, many of you, or most of you will be in very close proximity,. Given the liklihood of alcohol and the general desire to be boisterous at party; there
are reduced odds of compliance with masking; and/or social distancing even if room permits.
More people tends to require louder talking just to be heard (which may also precipitate the removal of masks, if otherwise worn) and increases the risk of transmission.
5) The secondary transmission from a gathering of size is exponentially larger; and much harder to track. Assume you have just 2 infected people who show up at your party.
There is a material risk they might infect the majority of your 40 guests.........it could be less, but you have to track down and test everyone to be sure.
That's a lot of work.
Lets assume that only 5 people were infected by each of the 2 people who arrived infected.
That's still 10 people total (not possible if your gathering had only been 4 people in the first place); but just wait......how many people have each of those 10 infected people had high-risk contacts with since they became infected?
While for some, it may be only 1-2 people they live with............for others.........they may have been at work, attended another party, or been on a packed bus without a mask on..
The risk factor is real that your one gathering may lead to more more than 50 cases; and more than 500 contacts by Public Health.
*****
Here's the thing.
I'm in favour of government being calculated and strategic in its choices.
I oppose blanket lockdowns for any length of time, for the simple reason I don't think people will adhere to them.
That said.........clamping down on large parties, private or public is one of the highest pay-off moves government could make.
We could reasonably argue about the size limit; or more extreme actions (household only).
But you can't reasonably argue that large gatherings aren't a material risk.
Because statistically speaking, they are.
They're also a royal PITA for Public Health to follow up on.