I very much doubt that will work. People will just install ad blockers instead. You'd be surprised what lengths many people will go to in order to avoid spending even $1. It isn't poor people either: in my experience the well-off who have time on their hands because they aren't busy living hand-to-mouth are more likely to spend a pile of their time instead of giving you that $.
In most cases it's just too unsimple/too expensive to pay $1, and especially recurring.
Look at how many people buy stuff in Free2play games, and it works because it's dead simple (enter your appstore password, click "confirm" and be done - and you can even disable the password verification). Time to buy literally less than 10s if done well.
Now compare this to a typical micropayment on a desktop site:
1) Payment provider forces autocomplete off => remember which email you signed up with
2) Payment provider disables password pasting => manually type in your secure 32 char password
3) Two screens of confirmations, if you're extra unlucky you have a two-factor stuff in the loop, too
4) Redirect to the original content (compared to mobile, where payment is an overlay)
Total time wasted: minimum 2-3min.
To make stuff worse: PayPal e.g. demands 20ct of 1€ transferred, and German VAT takes another ~15ct AND corporate taxes (assume them at 10ct, and even then it's low) - which means you're out 50% of the payment value after fees and taxes. Not very profitable...
Oh, and another thing I forgot: often enough even paying for a newspaper/service doesn't get rid of all adverts! In my eyes that's outright fraud. And even if services DO disable all ads, I have yet to see one that also cuts the data-milking tracker services. I paid for the product, so I'm NOT the product any more.
And it kills the values of the ads you do show, too, because suddenly the audience that sees them is limited to only people who can't afford or won't spend $1. Which is the exact opposite of the audience advertisers want to put themselves in front of.
Oh there will be some way of identifying them, surely?
If they are from people you have actively chosen to follow then the source isn't twitter anyway and you can just unfollow those users if you don't like what they post.
If they are extra items in your display then there will likely be some marker to pick up on. Even if not then someone somewhere will start a service where people can report advertising tweets so subsequent the plugin can remove those from the feeds of subsequent users who use the service... Or perhaps Bayesian filtering as used for email? Not perfect in either case but someone will try and have at least some success.
Of course if the paid posts are truly unidentifiable then presumably that look like they were posted/shared by someone they were not posted/shared by, in which case the service is completely untrustworthy and you should just stop using it because nothing it tells you na be relied upon.
Caveat: I don't use twitter and aren't particularly likely to in future, so I have no particular axe to grind here but might misunderstand how things work.