Not disagreeing or anything your comment just brought this to mind.
or a specialized market
Size is not necessarily a function of the word niche it only implies that the good or service being sold targets a group that is not a majority of all of the market participants. In twitters case 3.4B users on the internet, with only some subgroup that participates on social media and then only a subgroup of that group that wishes to participate with limited post length and then, business wise, just the business niche that have a large customer base within that subgroup of internet/social media/short form.
As an example BMW is a niche business, luxury auto, that had 92B in revenue last year.
Even that One Big New Thing they announced, namely Moments, still operated exclusively in that short messaging pubsub niche entirely (and turned out not to be something their users cared about that much so far).
Now their niche market seems kind of saturated, user numbers mostly peaked, and Facebook also started competing even more in that niche when they introduced searchable #hashtags and ways to follow accounts without becoming mutual friends, while still offering their other core features and "external" services like instagram (in direct competition to twitter) or whatsapp (in direct competition to twitter DMs). Tumblr is still there, which to me always felt mostly like a "twitter" for longer-form messages. I saw people switch from twitter to Slack (and recently Discord) and embrace their not-globally-visible pubsub models in some cases, so there is some competition there too.
So in conclusion: twitter seems to me like a pretty niche service (albeit large niche), and has competitors left and right now. It isn't in "that" niche, but in a niche.
Of course Twitter as a business did not have this choice - they had to go big or go home. For the founders though it might have been better to have built something else.
I doubt it. All of the founders are mega wealthy now both as a result of Twitter and other ventures. Twitter might not have reached the dizzy heights they aspired to, but like it or loathe it Twitter is a household name and the founders are "famous".