In MP-games I always take offensive, defensive, quantity and quality which only leaves room for four ideas anyway making the use of a diplo idea instead of an admin one useless in that respect.
In MP for DIP groups you're likely picking exploration, maybe trade, or nothing. In that case the ADM groups you'd select are Economic, Innovative, and Religious. These all have strong policies with the military groups you're choosing, each significantly stronger than expansion.
Which accounts for 7 of your 8 possible groups, or all 8 if you pick exploration. If you don't, expansion probably isn't helping you in the mid 1700's. The winner is likely decided, and colonies aren't going to be the difference maker if it hasn't been.
Like I said, they are good as a balance between trade and colonization for African countries like the Mamelucks.
Like I said, they are not. They are inferior to exploration in that role and lock you out of better policies/money making options in the ADM groups.
Sure optimal in it self is objective, after you have defined what you are optimising. As EU4 is a game I would prefer the idea groups to be optimised for fun. Fun is very subjective, and not defined as reaching a goal in the shortest possible time, even if that is how you personally have the most fun playing.
That's not making an actual argument though. For the idea group choices to be meaningful, there should be at least some plausible in-game scenarios where picking a given group is more attractive than alternative groups. By "plausible", I mean a situation you can realistically expect to see at least 1/10 games if picking a random nation. There are a handful of groups that are basically "never picks" outside of screwing around/strict roleplay.
I must disagree that the idea groups should all be balanced around WC or near-WC blobfests.
Expansion, maritime, and naval are still inferior even in crowded MP, which prevents anything even approaching WC. That's why the trash tier, they're nearly always bad. You're not seeing groups like economic, innovative, or quality getting called out with similar frequency because there are reasonable situations to pick these over alternatives.
It's not just about WC. WC is one goal towards which you can optimize. The trash groups fail to be worth considering for WC. But they also fail in general.
Trade especially allows you to siphon income from your neighbors and rivals, empowering you and weakening them.
The ducat value from that is small. The more attractive part of trade is something like economic/trade/quantity/quality where you have 20% more goods produced and 40% trade efficiency from the idea group + policies. If going the MP military route religious adds another 10% goods produced. If you already control a decent amount of land, generating nearly 1/3 a manufactory per province out of thin air and pushing the % multiplier from what you're collecting up can be attractive if further expansion is difficult or you need to bankroll a big alliance/major wars. This idea group combination already has a discipline policy (economic/quality), and with religious can add 15% morale.
Doesn't professionalism make aristocratic pretty competitive?
No, but guaranteed siege pip and an extra diplomat is pretty handy in SP once you have the most important expansion stuff. It's also the lone group that gives a RU policy with humanist rather than religious so can keep a trash religion from screwing absolutism.