Autocrats Love Liberal Democracy
Liberal democracies buy their stuff.
Liberal democracies provide a wide variety of opaque financial instruments to hide their wealth.
Liberal democracies sell them the technology and weapons they need to stay in power.
Liberal democracies abide by the rule of law, in other words with the right lawyers it is possible to get away with just about anything.
If things go south at home, somewhere in the liberal democratic world a safe haven will be provided for the right price.
What's not to love?