While I agree the duplicate use is bad in the OP, I disagree with your blanket statement that a module shouldn't be used twice. For example, my script and a module used by my script might both use FileHandle. It can even be acceptable within the same file. Consider a style I often use:

use Some::Module ();  # Don't import anything here.

# ----------

package Package1;

use Some::Module qw( ... );  # import something

...

# ----------

package Package2;

use Some::Module qw( ... );  # import something

...

# ----------

package main;

{
   ... main program ...
}
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One could argue this should be split into multiple files, but you'd still be including the Some::Module more than once.