Yeah. I agree. Getting a Jump on the Case does not seem to have much value.
I play a variant version of the rules myself. This alters the this quite a bit. I will try summarize this here:
Remove any hunch card for suspects not in the game, shuffle the remainder into the innocent(blue) deck, and deal one of each face down to each player. Place the remaining hunch card by the murder sheet face down. This represent the real murderer. Place the guilty (red) deck near the murder sheet.
GET A JUMP ON THE CASE (cost 1 AP)
If a player is in the same location as the scene of the crime marker, he mail secretly select any guilty (red) card from the stack. If he already has a guilty card he may replace it for another. At any point he may only have one guilty card. He may also remove the hero marker there and replace it with one of his own. If it is still in place at the end of the phase, he becomes the new first player.
CLOSING THE CASE
Turn over the hidden innocent card by the murder sheet. This is the real murderer. A player with a guilty hunch card matching the real murderer receives 2VP (even if he was killed my a hit).
Convicting the real murderer awards the player further 5VP (not possibly if he was killed by a hit)
… so with this variant, players will need to Get a Jump on the Case in order to pick who they think are the guilty. You can still get your usual points for winning the conviction of your suspect, but if you manage to also pursue and even convict the real murderer, you are awarded well. Since everyone knows for sure that their own innocent card is the innocent, you can consider if you want to let one or 2 players get their Jump on the Case first, and then try deduce the guilty. Finally, I think adding a few more points for solving the case, really put just a bit more focus on the mystery, which is nice. I use a few more variant rules, but this one can easily be applied on it's own.