i have shorter hair than he does是不是违背了 主语+be+比较级+than的结构?

没有.
主语+be+比较级+than 比较的是表语,表语是形容词.谓语就用be动词代替了.比如She is taller than me. My book is bigger than his. than 是个连词,相当于天枰一样,前后各种结构词性等要求对称.
i have shorter hair than he does . 有具体是使役动词了,have 翻译为“有”.有具体的动词就不用be动词代替了.