In order to produce HCO3- from glutamine and to subsequently reabsorb it, H+ ions need to be secreted. The kidney does this by via ammonium ions in the PCT. But why are the ammonium ions then reabsorbed in the TAL before being put back into the collecting duct? Wouldn't it be more efficient if they were just left in the tubule fluid where they would reach the collecting duct eventually? The first method seems to be a longer way of achieving the same result.
Isn't it all to do with the reabsorption of water, i.e. everything gets flushed out in the Bowman's capsule and then some stuff is reabsorbed to lower the water potential of blood, so water is reabsorbed as well.
I guess I figured it was easier to have a leakier sieve at the Bowman's capsule than try to only release the waste products via facilitated diffusion.
Why reabsorb $NH_4^+$ in the thick ascending limb if you're just going secrete it in the collecting duct
This is an excellent question. When you find an odd, seemingly inefficient aspect of physiology, it's an opportunity to learn something new.
This alternating secretion, reabsorption, and secretion starts to make sense when you look at the anatomy of the nephron.
There is no appreciable ammonia in the filtrate at Bowman's capsule (free ammonia is efficiently converted to urea in the liver by the urea cycle, so it's in very low concentrations in the blood). As you say, it is produced in the proximal convoluted tubule. The amount that is produced is regulated by the acid load (more acid, more ammonia production). The proximal tubule is in the cortex (top of the photo).
$NH_4^+$ is in equilibrium with $NH_3$ in the tubule, and renal tubular cells and junctions are relatively permeable to $NH_3$ here, so the more $NH_4^+$ is produced and actively pumped into the lumen, the more $NH_3$ backflow leaves the tubule and enters the ECF. Because of this, the primary work of the PCT in acid base homeostasis by the kidney is not secretion (though $NH_4^+$ is actively secreted here), but rather in the production of new $NH_4^+$ and new $HCO_3^-$.
The bulk of the work of secretion happens in the collecting duct. There are a number of passive and active transport mechanisms for the secretion of $NH_4^+$ here, especially in the medullary collecting duct. These mechanisms are aided by a high concentration of $NH_4^+$ and $NH_3$ in the medulla (at the bottom of the picture).
So where does this high concentration of ammonia come from? It's from the reabsorption of $NH_4^+$ in the thick ascending limb. This is reabsorption (the tubular cells take $NH_4^+$ from the lumen and send it to the ECF), but you can think of it more as taking it from the cortex and putting it in the medulla. The filtrate flows along the lumen of the tubule, toward the collecting duct. Much of it is in equilibrium between the lumen and the ECF before it gets to the thick ascending limb. At the thick ascending limb, the permeability of the tight junctions and the tubular cell membrane changes. Solutes (the one we're interested in right now is $NH_4^+$) are taken out of the lumen and left behind in the ECF. Because the filtrate flows but not the ECF, and because the tubular cells are permeable before the thick ascending limb, and impermeable after, this substantially concentrates these solutes in the medulla, and dilutes the solutes in the cortex.
This is a process known as the countercurrent multiplier. The same principle is used to create a hyperosmotic ECF (and consequently, allow for a hyperosmotic urine if you've been wandering in the desert for hours).
Here's a diagram of the nephron from a decent review article that illustrates each of these processes for ammonia handling: