What happens to coins that get sent to the Federal Reserve?

Found out my dump bank sends their coins to the Federal Reserve. Why are people happy when they discover this?
What happens to these coins? Is it because it takes a while for these coins to wind up in circulation again?
Or because the coins leave that particular searchers area and end up in another searchers box?
So far I have been dumping pennies on them. The largest dump I have brought them has been around $50.
I am scared to bring them $500 of halves at one time. But these halves would get sent to the Fed.
I have a half dump that takes the full $500 HAPPILY WITH NO QUESTIONS ASKED.
But I am 100% CERTAIN these are recirculated in the local area.
I want all the coins to GTFO of here so I can have brand new coins to search
What happens to these coins? Is it because it takes a while for these coins to wind up in circulation again?
Or because the coins leave that particular searchers area and end up in another searchers box?

So far I have been dumping pennies on them. The largest dump I have brought them has been around $50.
I am scared to bring them $500 of halves at one time. But these halves would get sent to the Fed.
I have a half dump that takes the full $500 HAPPILY WITH NO QUESTIONS ASKED.
But I am 100% CERTAIN these are recirculated in the local area.
I want all the coins to GTFO of here so I can have brand new coins to search
