My first thought is that the barrels left in the stockpiles have been claimed for other jobs, and that's why the brewers refuse to take and use them. Perhaps someone is coming to put things in them, or just move them elsewhere. They might've been repurposed for other stockpiles but the dwarves are filling them where they stand.
You might try setting the meals stockpile to have no barrels, having an entire barrel of food for every cell is a bit excessive anyway and may very well result in the pile only being partially filled, leaving many cells with no food in them.
Of course that's not an option for a drinks stockpile, but Tetty's suggestion to have a barrels-only furniture pile someplace may help get the empty barrels out and leave space for booze. That may also help get any barrel out before it gets re-claimed for other tasks, so that it doesn't sit on the food stockpiles in the meantime. Of course it's going to mean a decent bit more hauling.
This all usually works for me, I keep my prisons supplied in the same way, by making a big food stockpile that covers all the cells, removing bits of it until there's only 1 space of stockpile per cell, then repeating to make a drink stockpile right next to it. Very handy since I can then adjust settings for each type of pile wit one operation, instead of fiddling with each and every cell's food supply.
It may seem like a problem that each main stockpile can only have one other stockpile take from it, but if each of the stockpiles you want filled is for a different type of thing then it's much better that they each have their own source they're taking from. Otherwise, say if you could have a Booze pile and a Prepared Meals stockpile taking from a Main stockpile, and let's say you had lots of meals but not very much booze, the Main stockpile would end up completely filled with meals and Booze distribution would be uncontrolled.
It's better really to have a separate Meals and separate Booze piles, each placed where they can be easily filled up, that way so long as you have a decent supply of those things, the whole supply chain should work.
Whatever you do, don't make stockpiles infinitely (or excessively) loop around eachother, because so long as food or whatever is being moved someplace, it can't actually be used. So if you had Stockpile 1 at your farms, and it filtered down to Stockpile 15 or whatever at your dining room, you'd either have an army of busy haulers or a lot of starving, dehydrated dwarves. Not to mention a lot of unnecessary frame hits.