But if you get too rich, you can find inflation rising, which in turn can affect the stability of your nation. Many events, most notably wars and changes of religion, will reduce your stability, which causes knock-on events such as provinces being more likely to go into revolt. If you focus on fighting battles, it's very easy to let your ecomony slide while you're doing so. Of course, historically, many leaders did bring their nations to ruin by ignoring certain critical elements of their country's operations. It's easy to overlook remote colonies that should be bringing in valuable trade income when the enemy are at your gates with 50,000 men.
Diplomatic relations are of course important.
Your relationships with other nations will determine who is likely to gang up in an alliance against you. Many nations will have permanent grounds to go to war with you, just as you will have with them. Leading and managing an alliance can be a tense affair. Favours can be won with royal marriages, with token payments. But annexation and vassalisation are also common.