Princesses, how should we use them?

Lan is the best, although i only used Sakurako for the challenges in the crimean war, where i sold her immediately. As for the usage of the  palace as something static, it depends on how they are used. In hard conquests, building a palace seem counter productive, but by having that bonus 25% damage you can destroy anything with your cavalry. It's particularly useful in 1815 conquests from the coalition side, where you need to destroy the main french force. By playing defensive at the first 5 turns, you can counterattack with all your generals that are relatively healthy, while the main french army is destroyed, and all you have to do is to siege the cities before they can start spamming units again. Another scenario is using Sophia's 20% less damage to hold on to you capital that is under siege, so you can be sure that a militia will survive for 2 turns, and you can use your extra income for something else. For campaigns and challenges, they are really useful. Maria is useful in the challenge siege, while Sophia and Louise are just op. I think the best way to get my point is to see war games as not a static aggressive or defensive play style, but rather dynamic, where by sometimes playing defensive you achieve an aggressive goal(using sophia to hold on a major city so you can save money, thus using those to buy more useful units which in turn can be used to destroy the enemy faster), or playing aggressive to achieve defensive means ( Keep pushing towards enemy territory and capturing cities to prevent them from spamming units in those cities, and by making the enemy force focus on your generals rather than your other units/cities), or both at the same time (which is for the example of 1815 coalition, you destroy the main French force by playing both aggressively and defensively, using your cavalry gens to attack, but using them defensively in that you swap positions so they absorb damage for each other, thus having your generals as healthy as possible, so you can launch a massive counterattack that makes them capitulate before turn 25).