What's wrong with using backticks in a void context?

Strictly speaking, nothing. Stylistically speaking, it's not a good way to write maintainable code because backticks have a (potentially humungous) return value, and you're ignoring it. It's may also not be very efficient, because you have to read in all the lines of output, allocate memory for them, and then throw it away. Too often people are lulled to writing: 

    `cp file file.bak`;

And now they think ``Hey, I'll just always use backticks to run programs.'' Bad idea: backticks are for capturing a program's output; the system function is for running programs.

Consider this line: 

    `cat /etc/termcap`;

You haven't assigned the output anywhere, so it just wastes memory (for a little while). Plus you forgot to check $? to see whether the program even ran correctly. Even if you wrote 

    print `cat /etc/termcap`;

In most cases, this could and probably should be written as 

    system("cat /etc/termcap") == 0
	or die "cat program failed!";

Which will get the output quickly (as its generated, instead of only at the end ) and also check the return value.

System also provides direct control over whether shell wildcard processing may take place, whereas backticks do not.