So you’ve basically got three regions today with monarchies*- Europe, the Middle East, and Asia (East and Southeast); plus a couple in South Africa, as well as Morocco and Tonga, but we can put those aside for the time being.
Since Europe seems like the easiest (what with wwi taking out so many OTL), let’s start there - Britain, Spain, Netherlands, Belgium, Sweden, Denmark, Norway, Luxembourg, Lichtenstein, and Monaco - and divide them further into five categories of Britain, Spain, the Lowlands, Scandinavia, and tiny countries. Since the Spanish monarchy was only recently restored, we can put it aside easily enough; the small monarchies seem like they’d fall easily enough in time if they were to become the only crowned heads in Europe, so we can ignore them as well. The Lowlands were completely defenseless during the works wars, so having a foreign power overthrow their monarchies for good at some point isn’t difficult in the slightest. That really just leaves the OTL three royal houses of Scandinavia, which seem like it had a po if intersting potential in its own right, as well as one of our favorite AH tropes, a Republic of Britain (or a Republic of England, with Scotland and Ireland going their own way, whichever you prefer).
Then you have Asia - Japan, Thailand, Cambodia, and Bhutan. Like Spain, Bhutan’s monarchy was recently reestablished OTL, so we can check that easily enough. Getting a Republic of Japan seems like it should be doable independently, with a different end to WWII seeming like the most recent opportunity; Thailand I have no idea, and even less of one about Bhutan. The Middle East, in general, seems to have plenty of potential for wiping monarchy from the face of the region entirely - from the way the Ottoman Empire fell, to the potential of Nasserist and Baathist rebellion or invasion.
If we look at monarchies that have been abolished since WWII, it’s a fairly short list - Greece in Europe; Iraq and Egypt in the Middle East; and Cambodia and Laos in Asia. but when you look at the challenge here in piecemeal fashion like this, it becomes apparent that a world without monarchies is actually quite doable, even with a fairly late, post 1900 PoD.
*not counting countries like Canada who have their monarch based in Europe, who would most likely default to republicanism should the monarch in the “home” nation fall