One must realize that there were only two types of cavalry in Europa at the end of the Renaissance. The heavy cavalry, the descendent of the knights, were the main arm, with any type of lighter cavalry simply being cheaper and less elite cavalry, besides irregular cavalry like cossacks. It was not until the seven Years war that hussars came to be in Western Europa (Before that only existing in the Austrian army), and the first 'Chasseurs au cheval' or 'light dragoons' do not show up before the 1700s. Only after that, light cavalry can be considered a wholly independent arm of mounted forces, with their own role and tactics.
Dragoons are creating around the same period that the light cavalry becomes independent, as a mobile infantry force that did not require a lot of training on mounted combat. In the years, their focus lays more and more on being the link between the light and the heavily armored cavarly. Some sources, even in the Napoleonics, consider Dragoons to be medium or even light cavalry.
Anyhow, "the whole of Europa" did not change all of their cavalry to Dragoons. It's true that they often had the most regiments, like Sven said, being the sort of 'line cavarly', but hussars, chasseurs, light dragoons, lancers, cuirassiers and carabiniers were in abundance.
By the way, I do not agree with the statement 'most armies realised cavalry charges were going to become much less common'. That idea did not arise until the invention of Percussion Rifles.