Not just free platforms. No publication supported by advertising is a viable long-term solution let alone a desirable one. Advertising-based publishing was never a good idea. The current state of the press is a good example of that too. Unfortunately, there are not that many viable alternatives. People would pay for good journalism, not sure they would or should pay to reblog memes and other people's posts.
Define what you mean by “long-term.”
America has a number of ad-supported publications that have been publishing for over 250 years. There are probably older ones in Europe and elsewhere.
Indeed the ad-supported model is or was viable in print for a long time, although we started to see a shift there as well. Today the print media is struggling, ad revenue may no longer be enough to keep most publications afloat. The fact this model still works for some titles and was viable for centuries doesn't make it particularly good either. With an ad-based structure, the independent press ideal was flawed from the start.
I've always said that cheap is better than free. If all services like Tumblr had debuted at a nominal $0.25 or $0.50 a month and that had become normalized as a way to support the platform without mining data or being at the whims of advertisers, the internet might be in a better place.
Instead we have clickbait, engagement addiction and users as products and not customers.