When and if the Turkish armed forces enter Iraq and or Syria for real war and not a proxy war or for training people in camps, then some will realize the difference and their own insignificance, till then it is merely a pissing match of who pees further... the amount of soldiers that Turkey can put into these countries are more than a thousand times more than the US ever could put into them, that is before I begin to mention Turks not being strangers to the area and people, favorable terrain and morale against both places and against those who are available to fight on the opposite side,
( i.e. ISIS/DAESH is merely a tiny force, and yet it is holding for so long large parts of both these countries, and causing casualties in skirmishes against all of these US uniformed and armed 'cool' looking useless soldiers that run time and time again leaving their weapon behind... ) and lastly the non-existent air-forces or real armed forces of these countries..
Yes sure it would probably be a bloody war, and Turkey will probably loose 100K+ soldiers, but when has that stopped the Turks? It took ~40K Turkish troops
(that were poorly armed in comparison to their current state) to go over a mountain range, and clean out the North of Cyprus in 1 month, that against an enemy of similar size, and which surrounds two sides of Turkey... with 498 soldiers lost, 1000+ wounded, and a embargo against Turkey after that, which continues to this day in form of EU talks blockades.
In both Iraq and in Syria there will probably be a lot more locals supporting Turkey, even if some Turkish allies suddenly go enemy, others wouldn't, so unless they want to go WW3, it will always be a stalemate, which means response against Turkey would be an embargo and not war from them. Other considerations are Iran or Arabic countries, would they go to war with Turkey? directly, I doubt it.. indirectly definitely, but their proxies aren't really up to the task.
So considering that this whole thing will be extremely ruthless, yes, I would say that Turkey "steam rolling" or "flattening" countries if it declared an all-out war is a correct phrase.