It may be a better model for something, but it's impossible for this to be used on a "reddit-like" site.
Reddit is a large community where many users are anonymous. A paid model means it will never be a large community and posters will never be anonymous.
And while reddit has tried to make freemium work, I'm pretty sure it has never worked and their real business model is ad based. Advertisements are a centuries old model that has proven to work well, I encourage you to switch to that (and on your API, make it a requirement to show ads).
Also don't allow people to remove the ads by paying - you need to show ads to people with enough money to buy the stuff you're advertising. Exclusively showings ads to poor people does not work. Just make sure your ads aren't annoying.
It's your site, you can do what you want with it, but it won't be like reddit with your proposed business model.
...to you. Not to reddit themselves in virtually all cases. Maybe 1% browses through seven proxies but if the 99% is okay with "public anonymity", it'll work for the masses so long as you don't show everyone's payment details on their profile pages.
(Whether excluding this particular 1% desirable, is a different question.)
I would definitely not pay money to a site that wanted to show me ads, regardless of my preferences, as a subscription member. Full stop.