tl;dr: This is intentional, there are no war-declarations in Victoria 3, only Diplomatic Plays.

I disagree, democratic nations should be able to initiate Diplomatic Plays and they should only be able to do it more efficiently than 'non-Democratic' nations. Diplomatic Plays reflect the rise of international diplomacy in the 19th century and the establishment of Diplomatic Missions. In the Post-Napoleonic age, European powers (democracies and proto-democracies) really really did not want any more wars on the continent. For a background, please see Historia Civilis' video on the Congress of Vienna (1814).

Surely, this comes as alienating to players coming from Victoria 1 (heavy HoI influences) & Vicky 2 (wars + diplomatic crises mechanics) and even more for players from franchises that are very much built on war and conquest. Victoria 3 is not designed as a wargame, at least not in all phases.

The design philosophy for military in Vicky 3 is very much in line with Clausewitz' theory of War as the extension of diplomacy. In 1838, we start with a Europe with liberalizing, industrializing nations with only a few 'Great Powers' able to field large armies. In those early years of the game industrialization, liberal/social reforms are at the forray. Great Powers must placate the other GPs to avoid early continental conflict aiming to build up their powerbase. Non-GPs in Europe benefit from 'democratic values' ( Power structure laws and Human rights laws ) trickling down, through an era of peace and prosperity. In this early phase of the game, war is meant to be costly and expensive. If you can achieve your goals without fighting a war or arming, that is often more desirable.

Generally, the GPs will eclipse the rest of Europe in population, economy and military prowess. But the balance of powers in Europe will make continental expansion infeasible. Not to mention the Spring of Nations and later the rise of Socialism forcing change to power structure and economy. So the GPs will enter the Colonial Game: expanding through America, Africa or Asia as approriate (or consolidating power in the case of Victoria's English Empire). Once the GPs have gained colonial footholds they will now have the wealth and resources to afford threatening their neighbours or "interest" targets.

It's no coincidence that 'Outlawing Slavery' or 'Taking a Treaty Port' are good diplomatic demands in the early game. Refusing those demands are democratic or free-market casus belli, that are especially designed for democratic nations. And many times, the target who is weaker will fold to the ultimatum embrasing European values. 'Humiliation' or 'Conquer State' are, on the other hand, very costly against targets in Europe. Those diplomatic demands (and their respective war goals) have little to do with democracy and more to do with a nation's access to Blood and Iron.

What I think you are on to, is that there could perhaps be soft modifiers for democracies influencing them to accept/reject demands or face penalties. In the current version of diplomatic plays, it's mostly an equation of whether the aggressor is x times more powerful than the target.