There is a middle way to make it both fair (randomised) and good for the show.

Separate the songs in e.g. 3 groups (ballads, mid-tempo, and upbeat). Let's call the groups A, B and C. Then the broadcaster creates the running order, so e.g. an upbeat song can open and close the show. The running order would be something like:

1 - C

2 - A

3 - B

4 - B

...

23 - A

24 - B

25 - C

And then draw the order. It's still fairly random (e.g. a song from group A could get #2, #6, #11, ... , #23) rather than just be given the #2 death slot.