It's true that for a long time British accounts lionised Wellington and largely ignored his allies. Thankfully in more recent times that imbalance is being redressed and Wellingtons allies are recieving more of the credit they deserve.
But for a great many people, both in Britain and outside of it, people who have no particular interest in the history, the older innacurate version of events may be the only version that they know.
The arrival of the Prussians was indeed a crucial element of the allied victory, but so too was the part played by Wellington and his army. If Wellington had not nailed himself to his ridge and weathered the storm unleashed upon him then Blucher would have had nowhere to go except retreat towards Berlin as Napoleon had intended.
That said, we have to recognise that Wellington was dependant on the Dutch, Belgians, Nassauers, Hanoverians, and Brunswickers in his army. Had he been restricted to only the British, or even the British and KGL battalions he would not have had the numbers to even consider making a stand against Napoleon let alone endure a whole day of the most intense punishment.
Also a short time ago we discussed the importance of the actions of the Dutch/Belgian/Nassau troops in holding Quatre Bras while Wellington gathered his army.
So the only troops not crucial to the allied victory were the Duke of Cumberland's Hussars. But I still think Wellington was the architect of that victory. He chose the ground, he forged the link with Blucher, he deployed the army in a fashion that would give stability to the large number of green troops. I don't think it would have done had he not been there.
I read recently that French troops of the time were fanatically loyal to their Emperor and attributed any mishap to treason. It's interesting that this belief persisted, but I can't agree that Napoleons subordinates were responsible for his defeat.
Certainly Ney might have done more at Quatre Bras if he was not Ney, and Grouchy might have done much more at Wavre if he had the inclination. but both were acting in accordence with Napoleons orders.
It was Napoleons aim that Ney should hold Wellington in place while Napoleon defeated the Prussians and that Grouchy would persue the retreating Prussians while he dealt with wellington. That the two armies would be seperated and retreat along their own diverging lines of supply thus alowing them to be destroyed in detail.
Napoleon seems to have been convinced this was how things would happen, because he had ordained it so, and made no contingency plans for the unlikely event that Wellington and Blucher might not read the script.
Ney and Grouchy failed to adapt to changed situations. So Ney held Wellington in place even when there was not much of Wellingtons army to hold. And he held Quatre Bras when he could have persued Wellingtons retreat.
And Grouchy persued the Prussians,In a desultory fashion, when he might have tried to come betweeen them and Wellington or marched to Waterloo himself. But Napoleon should have covered any eventuality in their orders. He was in overall command and the ultimate responsibility was his.