This sorta happens. I'm not sure that it immediately happens, but take into account that your flags per day are increased based on your flag weight increase from 100 to 500. You get one additional flag per 20 flag weight, totalling +40 flags per day when you hit 500. That's basically one new flag per 2 valid flags for your first 80 flags. As well, you get another flag for every 2,000 reputation you have (capping at +50 at 100,000), meaning a minimum of +5 by the time you can access the flags tool. This tops off at a total of 100 flags.
That's a lot of flags per day. Now, not everyone is going to be remotely at 100,000 reputation, and I can respect that, but even without reputation, the enthusiastic flaggers are generally already at 500 flag weight and have at minimum 55 flags. That's more than the number of close votes you get, which was upgraded twice!
It's definitely an appreciated effort, what people go through in flagging. But that's seriously a lot of posts to burn through. I think it is a healthy thing to take a break, much in the same fashion we have all other forms of rate limiting. We don't refund close votes for successful closures, we don't refund your questions per day based on how awesome they are, so my personal thought pattern is that it's a rate limit we should respect. After all, if so many users are burning through their flags so fast, then there's definitely enough people to cover for you once you've exhausted your own supply.
I think Stack Overflow is the only site which has even remotely the volume of flags where multiple users will be running out of 50+ flags every day. This kind of feature will barely see any use on the majority of sites where an average user rarely burns through their default daily 10 flags over the course of a whole week.
It's not unheard of for Stack Overflow to get special treatment due to its volume (like the front page change), however. I'm not a fan of more differences between sites that make it more difficult to explain rules (especially with something that is an entirely different mechanism of operation), but if Stack Overflow really needs it, then it might not hurt to make it specific to there. But outside of Stack Overflow, I don't think there will even be a visible impact.