So then the question is, if a tower is holding 10-15 drives, why would that be any less heat or noise than the aforementioned rack server?
-superboyac
It can be as loud. But it doesn't have to be. You're not cramming as much into as small a space - and you can take noise into consideration. Something the rack case designers definitely do
not.
The other problem with rackmount is the form factor. Out of the rack, they're the size of a mutant pizza box -as this snapshot of a 1U server from one of "Levi the Computer Guy's" videos shows:
They look pretty svelte in the rack. But out of it they're something like 17"x28." And once loaded, they're unwieldy and drop prone if you're not expecting the weight or really weird balance. I'm no wimp when it comes to lifting things. But the first time I pulled a 3U ProLiant server completely out of it's rack, I almost lost it. And that puppy only had 6 drives in it.
One thing that complicates your design spec is needing to have removable drive caddies because you anticipate so much swapping in and out. If you get away from that slightly, the Lian Li "A" series has been a popular go-to choice for multi-drive server configurations. These cases are specifically designed for this purpose so they've engineered for adequate cooling and airflow. The
Lian Li PC-A70F and similar are good choices. That could give you 3 externally accessible slots for tray mounted drive bays along with seven internal bays for the more permanent drives.
Lian Li makes a nice case. But they're expensive.
Something you might want to consider since you're an engineer...maybe design your own and have a sheet metal shop fab it for you?
If you're not doing a data center, why bother cramming stuff into the smallest case possible? You're only going to have one of these, right? (Right?
)
I always though a case with staggered and spaced drives with large slow fans on top and bottom would provide vastly better cooling and less noise than traditional drive array cases. Possibly even metal grill (less heat build-up) if it didn't dissipate the airflow too much before it passed over all the drives...
Something like this very rough sketch:
I once joked I'd like to use one of those Dysan bladeless fans for it.
Hmm...not too much a joke now that I'm thinking about it.
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You are crazy. But you're my kind of crazy,,,) 
I'm impressed every time. Very clever insight he had about it being the fan motor, and especially the blades that are responsible for almost all the sound emanating from a fan. Something military submarine designers figured out years ago when they addressed the similar problems of engine noise and propeller "cavitation." 
