Thinking about it, I actually kind of do like the last-hitting mechanic. However, I think there could be room for improvement.
For example, still granting some gold for being near a minion that dies, even if you didn't last hit it. If this amount does not affect the amount of gold the last-hitter gets, it would allow supports to get more gold for being near the fight, for example. It could also perhaps help make melee champions viable in more lanes, since even if they get harassed away from the minion wave, they can still get some gold.
Also, perhaps a reduction of how much gold minion gives, in proportion to how much gold you get for killing champions/towers. Even small changes to the ratios between these gold sources could perhaps encourage more aggressive plays. But it couldn't be too much of a change, or else farming minions would no longer be worth it.