But I wouldn't want to scrap the rival system completely. While I find it way too static in its current iteration, there is historical precedent for long-term rivalries. Eg: England/Britain and France, or France and Spain, or France and Austria, or Bahmanis and Vijayanagar, or Persia and the Mughals, etc. What I would like is a timer for rivalries, probably based on the magnitude of the conflict in the ambitions/missions. If the ambitions are more regional in their character, then the rivalry exists for around 30 years (arbitrary number, but can be tweaked to get the right balance). For larger ambitions, like Britain's ambition of preventing a hegemon on the continent, the rivalry with France could last 200 years (again, arbitrary and requires tweaking). And the end of the rivalry can lead to a period of cool-down, probably designed as a ticking opinion-modifier titled "Former Rival" last for a couple of years.
Britain and France weren't rivals just for the heck of it. If we were to put this rivalry in the context of your and mine idea, it would go along this route:
1) England has the ambition to form a PU with France; hence Britain and France become rivals
2) England and France then both have ambition to form colonial empire; hence they become rivals
3) Britain and France both seek to dominate European diplomacy and become the preeminent European powers; hence they remain rivals.
However, then the following happened: Prussia defeats France and becomes the dominant power in Europe.
Now, England's principle rival in Europe is Germany, not France... Now, Germany's ambitions now become "to have the best army and navy in Europe and expand colonial empire". This puts them directly in conflict with both Britain and France. So, Britain and France now suddenly become Friends driven by the common ambition to bring Germany down.
Under EU4 rules, or, for that matter, any rules in which countries choose to become rivals by choice (rather than necessity) such a Diplomatic realignment will never take place).
France - Austria rivalry can, similarly be explained; up until Austria remained the most powerful German state, they were France's rivals. The moment Prussia defeated Austria in the War of Austrian succession and took over Austria's status as the most formidable German military power; it was Prussia who became France's rival, and Austria allied with them; just like that.
So, what I would like to see, is that the system be changed from nations designating other countries as their rivals to nations designating their short/medium/long term goals and ambitions (how many can depend on the size of the country, options, game balance etc) and rivals being generated for the country automatically depending upon their selected ambitions (and the ambitions of other countries which affect them)
The Power Projection system can be woven into this -- the more ambitions you achieve -- or the more you progress towards your long term ambitions, the more PP points you will get. This totally makes sense, because by definition, you will achieve your objectives directly at the expense of your rivals.
This will also allow for changing rivals based on changed political circumstances without you changing your ambitions. For example, if I am playing England and one of my ambitions is to dominate the Eastern America colonial zone, and Portugal is the other country in that colonial zone; they would become my rival. However, if they go to war against Netherlands and Netherlands manages to takeover all their provinces in the Eastern American Colonial zone, my rivals would automaticallly change from Portugal to Netherlands because now it makes no sense for me to be anti-Portuguese, we have no quarrel.
