I disagree with what your saying because the Dothraki don't storm castles they essentially run a scorched earth campaign and have no equal in the open field. The Dothraki also would have the largest force which is reported to be with 100,000 men with most of them on horseback. Then the Targaryens would have supporters in Westeros who would rise up to join their cause and you know how fickle the kingdoms are just ready to join the winning side. For example the Tyrells.
Scorched Earth only works if you can besiege the castles and prevent resupply by sea. The Dothraki can do neither.
Alliances are great when you can get them, but an army of foreigners, speaking a foreign tongue, with foreign gods, burning and pillaging everything is not the best way to make friends.
Westeros isn't all open plains. Light Cavalry is a poor strategy in forested or mountainous areas like the North, the Stormlands, the River lands, Iron Islands, or the Mountains of the Moon.
No Dothraki army could ever take the Vale.
Dothraki are ill prepared for even a mild winter.
Compound bows lose their effectiveness in humid weather, making Dothraki horse archers far less effective against heavily armored knights.
Sure, you can harry the small folk and the lords dumb enough to leave their castles, but like Hannibal, unless you can storm the walled castles and cities, you're never more than a nuisance.
In the war before people didn't siege storms end they were getting starved out. I can't remember if that was the Greyjoy rebellion or when Robert battled the Targaryens but Storms End was going to fall if Davos wasn't able to sneak in food for Stannis and his men.
because Storm's End could not import the food due to being invested by sea, a capability the Khalasar does not have without a navy of fighting ships. Transports cannot effectively close a port to shipping. Storms End would have just imported food by sea and continued about their lives while the Dothraki starve and freeze outside the gates from burning everything.
This post was edited on 4/8 at 2:29 pm