Why $H_{V^* \cup W^*} > H_{V \cup W}$ if $H_V$ denotes entropy of language

Question

Let $W \subseteq X^*$ be an infinite language over a finite alphabet $X$, and define ($|w|$ denotes the length of $w \in W$) $$ H_W := \limsup_{n\to \infty} \frac{\log_{|X|} | \{ w \in w \in W, |w| = n \} |}{n} $$ the entropy of the language. Then of course if $U \subseteq V$ for two languages we have $H_U \le H_V$ as $V$ has at least at many words as $U$ of each length. But if $H_{V^*} > H_V$ and $H_{W^*} > H_W$, why do we have $$ H_{V^* \cup W^*} > H_{V \cup W} $$ where $V^*$ denotes the Kleen-star $V^* := \bigcup_{n=0}^{\infty} V^n$.