There's another aspect of realism that Martin ignores here though.
Just like IRL Mongols would have had a hard time doing their usual horse archer song and dance within the confines of Europe, with all its rivers, dense forests, hills, mountains and castles, so would the Dothraki face the same issues in Westeros. It's the reason Parthians were never actually able to attack too deeply into Roman territories, while Romans could and did bring the fight to them by not engaging them in the field and just rushing for their cities.
The Dothraki would likely fare much worse than actual Mongols, who did employ heavy cavalry, infantry and siege engineers to supplement their armies.
And this is all once again ignoring the logistics of such an army. Each Dothraki likely has multiple steeds to be able to keep up a speedy advance, probably 3 to 4 - now imagine having to ship such an army across the sea, horses and all, and then keeping them supplied in the field. Plus, they're basically useless in sieges.
Yes - all the great Eurasian steppe hordes which actually made an impact on the course of history were very much adept at absorbing those they vanquished into their ranks as auxiliaries, bringing their own talents & expertise to further empower the horde and basically letting them snowball against progressively bigger & stronger enemies. Attila's Huns were very much not just a horde of Huns by the time they hit the Western & Eastern Roman Empires, at that point the Huns were ruling and recruiting from a huge mass of East Germanic (Gepids, Goths, Heruls, Scirians, etc.) & Sarmatian (Alans, etc.) tribes. He recruited Romans as well - for example Flavius Orestes, the father & puppetmaster of the final Western Emperor Romulus Augustulus, was a Pannonian Roman who served Attila as a court secretary between 449 and 452 AD, and Roman engineers were probably the ones who built him rams & siege towers to attack Roman cities with (as the Huns having such siege engines was reported as a new & concerning development by Roman sources of the time).
The Mongols did much the same to conquer China. The Song dynasty in southern China had all of Europe's advantages on paper and then some; very rough terrain (loads of forest/jungle, mountains and massive rivers) where horse archer tactics would've been less effective, immense fortresses, a ridiculously huge population (they're Chinese so that's to be expected) and on top of it all, they also wielded gunpowder which the Europeans didn't have at the time. Kublai Khan overcame all of the above by using a mostly-Chinese army & navy, raised from the northern Chinese territories he & his predecessors had already conquered, such that the Yuan conquest of the Song looked a lot more like one Chinese empire conquering another than the Mongols riding roughshod over the Song while throat-singing. A serious Mongol push into Europe would probably have resembled a blend of their own approach to China & the Hunnic invasions from 800 years prior - using buckbroken conquered peoples like the Cumans and Russians to push against, say, Poland and Hungary (which they already did successfully IRL, they just didn't stick around), then recruiting buckbroken Poles & Magyars to sustain their momentum against the HRE and so on, not a swarm of horse-archers camping around & needling German castles (at least not JUST that).
Of course, in yet another failure of worldbuilding, Martin's Dothraki are never once shown even trying to assimilate conquered foreigners into their ranks & employing them as auxiliaries on any meaningful scale. They destroy every town they come across that can't fight them off, wiped civilizations like Sarnor off the face of the planet instead of making even the most basic effort to try to understand & integrate them as the Huns did with the Romans or the Mongols did with the Chinese, and not only do they always take the plundered idols of their enemies back to Vaes Dothrak as trophies (whereas real nomadic empires were generally pretty religiously tolerant)
but the Great Stallion religion actually commands them to destroy all signs of civilization (not just cities, even simple farms & plowed fields are not to be spared) to heal Mother Earth (thereby making ANY sort of coexistence with settled civilization functionally impossible). Add it to the pile of reasons, alongside their '''''tactics''''' and lack of armor, that they really should not be a threat to anyone who's progressed past the Stone Age technologically & socially...
Now, GRRM has said that he didn't just 'loosely' base the Dothraki off the Mongols, Huns & other Eurasian steppe hordes, but also the Plains natives like Comanches & such. Which makes them being so pointlessly, ridiculously destructive and hostile to anything resembling post-Stone Age civilization make a little more sense, since peoples like the Comanche really were horrifically brutal & destructive prairieniggers lacking the refinement & social adaptability of the Eurasian nomads IRL.
However, gunpowder aside, the Plains Indians never managed to establish a nomadic empire of their own which didn't melt away before the power of their settled neighbors (namely, 'Murica) and their general inability/unwillingness to integrate conquered peoples (just other natives, not even talking about any European settlement they might've conquered here) massively kneecapped them by providing Uncle Sam with no shortage of rival native tribes who'd happily sign up with the Indian Scouts to buckbreak their enemies & tormentors (for example, the Crow fought
for the US against the Sioux, the Tonkawa against the Comanche, etc.).
Yet despite adopting their most brutal & ruinous habits, the Dothraki never suffer the consequences that realistically followed for the Plains Indians. Hell nobody is mentioned to have so much as tried turning one khalasar against another (whether with financial bribes, a strategic marriage, whatever) in the history of Essos, even though khalasars are known to fight one another and it's literally the #1 most obvious trick settled civilizations would use to divide & - if not conquer - then at least manage hostile nomads on the horizon (America nothing, China did it all the time with the Mongol tribes before Genghis unified them, for instance). Even Dany's marriage to Drogo is, of course, supposed to facilitate a Dothraki invasion of Westeros and consequent Targaryen restoration rather than bringing peace or an anti-other-Dothraki alliance between Pentos & Drogo's khalasar.