In April 2023, the newsletter platform Substack received an unexpected proposal from Elon Musk, who had recently purchased Twitter.

Mr. Musk put it plainly: He wanted to buy Substack. At the time, he was trying to supercharge paid subscriptions on the social network, now called X, which had long fashioned itself as a “global town square” for political news and debate. Paid subscriptions are the core of Substack’s business.

He floated the acquisition on a call with Chris Best, chief executive of Substack, suggesting that Mr. Best could serve as chief executive of the combined company, according to three people familiar with the conversation.

Mr. Best declined to entertain the proposal, and the short-lived discussion ended, the people said. But in the aftermath, Substack crystallized a new mission: luring politics obsessives away from social networks like X.

Tens of thousands of free and paid newsletters are published on Substack each day on topics as varied as salad recipes, Bitcoin strategy and vintage fashion. But in terms of readership and revenue, the platform’s most prized category is politics. Increasingly, Substack has been selling itself as a home for cogent analysis and civilized discussion — an alternative to the decay of social media discourse.

“There’s a desperate need for a quality platform with trusted voices, where honest-to-God political discussion, debate, disagreement can happen without it either disappearing into the ether or taking place on a platform where there’s constant knife fights and flame wars,” Hamish McKenzie, a Substack co-founder, said in an interview.