Basically, friendly and allied status. They're done in the tenths, but with influence scaling, diplo units increase in the hundreds.
Comparing them to missionaries is fair. Without the extra cost for missionaires, they'll be spammed everywhere. To much unit management for people and for PC memory.
Diplo units are restrained by the availability of paper. This change is what made diplo spamming bearable. But the requirements for paper only increase with the advent of new diplo units. So, crazy idea here:
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1st. Make paper requirement for diplo units increase with era.
Ancient-Classical, require 1 paper each unit. [...] Modern, require 4 paper each diplo unit.
2nd. Make national diplo wonders give more paper at key technologies.
Thus, delaying the diplomatic tech is pointless, as paper is hard to get by and it could result in diplo units not being able to produce due to the lack of paper.
3rd. Make better diplo units very expensive.
This is a boost to wide play. Wide civs have more gold, so they can purchase diplo units very often, while tall civs are usually better producing them, which means precious production turns invested in diplomacy. The technologies cannot be avoided, since it would make it impossible to produce units.
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As it is now, tall civs have spare paper, thanks to extra great diplomats and diplomatic wonders. They could sell it to wide civs, or negate them the resource.
Too much new code.
Don’t forget missionaries use faith not production. Not comparable in value.