How would you know what they would want to do?
You try to doubt that there are would be any motives and then you say, it would probably be good PR?!
You question the quality of these startups, like there are no good startups outside YC, when at the same time my suggestion included that there should be the prerequesite of these startups to meet YC's expectations.
And if you call it 'open house' instead of 'open investor day' how that makes it different?! You are talking about the same thing...
Except, if by that term you mean a place for people to gather around and talk. I think thats why they already have Startup School and YC News...
Of course, it doesn't necessarily need to be the specific investor day, but instead maybe one divoted to their YC online community..
The essential motive would be that their YC ecosystem can continue grow outside their boundaries, while giving the opportunity to people that could probably proof capable enough. And maybe minimize the error of the application process.
And I did say, there could be a trade-off in percentage of the company in case it finds an investor through YC.