First my opinion, and then the data (on SO, and only insomuch as I can give you).
From what I've seen on Stack Overflow, the tying of moderation activities to a gaming aspect of the site severely hampered the moderators in their ability to moderate effectively.
On a fundamental level, the gaming aspects and the moderation of the site are diametrically opposed to each other. A moderator's first responsibility to any Stack Exchange site is to the content (making the Internet better), not to the game. The gaming aspects provided by the system are there to provide an incentive for users to that end as well.
However, as moderators, we sometimes have to take action that has an impact on the game (converting answers to comments, deleting answers, deleting posts, CW conversions, etc.). While that usually has an unfortunate impact on the game for someone, until flag weight, the worst impact was incredibly minimal, and it was almost always something that could be overcome easily by simply trying again.
All-in-all though, we had little impact on the actual game and we could focus on the primary goal of the site; curating great content.
When flag weight was introduced, moderators became the singular source for the minimal benefits and drastic penalties of that gaming aspect of the site. Granted, we should never let the gaming aspect of the site prevent us from the primary goal (curating great content), but as we've all seen, there were numerous posts on meta regarding the rejection of a single flag.
Granted, every user on Stack Exchange is completely justified for asking for an explanation for a moderator action on meta; unfortunately, the driving force behind these questions generally wasn't to further the first goal (curating great content) or out of a desire to understand how we work to achieve that goal, but usually out of a desire to further themselves in the game.
An additional impact was the ordering of the items in the flag queue; because flag weight contributes to the order of items in the flag queue, moderators were seeing flags whose order was contributed to by a metric that was meaningless.
All-in-all, this placed a tremendous amount of pressure on the moderators to place more emphasis on the (distant) secondary goal (to play referee for a specific gaming aspect of the site) of the Stack Exchange sites, instead of the primary goal (to curate great content).
Now the data.
From what I've seen on Stack Overflow, the removal of flag weight as a gaming mechanism has had a tremendous impact.
First, I can't recall a single post on meta asking why a flag was rejected since it's been removed. Why would it? If a flag was rejected, they simply had to try and flag again; the severe penalties are no longer there.
This means that there is less noise on meta, and that's a good thing, as it allows the moderators to focus on the primary goal of the Stack Exchange sites.
Additionally, it's allowed us to effectively use the rejection of flags as teaching moments, taking action (or none) where it was needed and conveying to the user that the flag was incorrect (and possibly why depending on the rejection reason).
This will eventually lead to better quality flags over time.
However, on Stack Overflow, from what I've observed of the flag queue, the sheer number of flags are typically triple or quadruple the number that I typically saw from the time I was elected in November of 2011.
Granted, we've been able handle them, but to me, it seems people are flagging much more with generally good results.
To your point about missing the kick of gratification, from my perspective, you are an outlier in that regard, as I've seen a few individuals go absolutely nuts with certain types of flags, unearthing dark, horrible content that I didn't know existed in the bowels of Stack Overflow.