And yup, definitely a concern. Makes me think that perhaps there's a possibility to not cap the posts, but rather have any posts outside of the first one in a week have something like a "secondary" tag. Then again, you might run into the problem that Instagram has where everyone stopped posting as soon as stories caught on.
Alas, it's a tricky problem.
In doing so, there would be no real scarcity for the writer (the post can be edited to the infinity) and you encourage writing long prose.
Your UX should show that editing the post is the default option and publishing it should be some ritual (maybe send a notification when it is possible?)
Anyway, love the idea. Good luck!
Say I post something about my weekend on Monday, it could be important about the loss of a family member or the birth of a child. Maybe I don't want to wait a number of days for that to appear on someone's feed...
But I could also post something new later that week. If it was consolidated into a weekly post it'd end up more like a digest at the end, and someone logging into the social network on Friday would see everything that happened to me so far that week.
It's a play on some of the ideas others have had, but the trick is timing. If my posts are digested to a weekly summary, it's going to reduce incentives for anyone to log in and use the platform on any day but "post day". Additionally if I'm free on Friday to spend time on there, but your new digest won't be posted until Saturday, I'm going to miss everything that's happened to you all week.
I'm sick of articles needing follow ups or corrections instead get a separate, unlinked post.
Articles become stale but they get shared and referenced as if they're the final point on the subject.
Maybe new users can make secondary posts, and as they post more and connect with people, you guide them somehow towards 1/week. Sort of reversing the traditional pattern that new users might need to be rate limited when they first sign up, instead what you want is for established users to post slowly.
That said, it is important how the posts are presented. A person who posts all the time about each plate of food... might not be as interesting as another friend who writes only once a month, but usually about really interesting things. A good UI which puts control in the hands of the consumer (but easy to use - convenience matters) is the most important thing here imho.
Best of luck!
It might very well be that the best social media is simple private messaging.
It limited the amount of friends you could have. As a result, people didn't add friends because they didn't want to give up a space for a potential future connection. The scarcity worked against Path.
You might find the same result where people won't post because they'll be afraid of using up their allotment when they may have a better one later.