The Hanbali school is the youngest of the main Sunni Islamic schools of jurisprudence, but more importantly, the Hanafi school was the official school of the Ottoman Empire - hence, its vast geography - while the Shafi'i school continues to dominate in East Africa and Southeast Asia primarily because of centuries of ties between these two regions via the Indian Ocean (though from what I understand the origins of Islam in SE Asia are still fairly murky to historians) and the Maliki school retained some dominance in North Africa and some of the Arabian Peninsula against the Ottoman Empire, whose power and control over local populations waxed and wanted depending on time and place.

Where does this leave the Hanbali school? Well, many followers of that school were banished in the 10th century CE by the Abbasid Caliph Al-Radi from Baghdad - at the time, the capital of the Caliphate - because of their dogmatic (often, violently so) opposition to both Shiites and fellow Sunnis who were suspected by some followers of the Hanbali school of being "deviant" or "sinful" (note that the Hanbali school, as you mentioned, is dominant in only three Sunni Gulf monarchies - especially the Kingdom of Saudi Arabia. That's not really a coincidence, if you consider both the overall forms of Sunni Islam dominant in those states as well as the long-term consequences of the events in the 10th century CE that I described above...).

Also note that the aforementioned events in the 10th century Abbasid Caliphate took place well before the rise of the Ottoman Empire and the continued resilience or even spread of three largest schools of jurisprudence - especially the Hanafi school under the Ottomans, as I mentioned before. That being said, the Hanbali school is pretty widely accepted as a perfectly legitimate, mainstream school of Islamic jurisprudence within the Sunni world.

Hope this helps.