Unicode has all sorts of features: combining marks, bidirectionality, input methods, surrogates, Hangul syllables, etc. Isn't a big burden to support?

Unicode by itself is not complicated to implement--it all depends on which languages you want to support. The character repertoire you need fundamentally determines the features you need to have for compliance. If you just want to support Western Europe, you don't need to have much implementation beyond what you have in ASCII. Which further characters you need to support is really dependent on the languages you want, and what system requirements you have (servers, for example, may not need input or display). For example, if you need East Asian languages (in input), you have to have input methods. If you support Arabic or Hebrew characters (in display), then you need the bidirectional algorithm. For normal applications, of course, much of this will be handled by the operating system for you