The problem with using a NAS as you envisioned is that a NAS works around the idea of seeing your drives as a single volume or pool, so if you pulled one drive out, swapped another drive in, then it would rebuild the array. Depending on how many drives, total volume size, which RAID, etc., the rebuild can take many hours or even days in some cases. The other issue is that rebuilding arrays puts stress on the drives, and doing this routinely rather than (as intended) having it as an option for if a drive crashes, could cause the other drives to run into issues from doing the rebuilds. It's not something you want your NAS doing regularly because there's just so many variables and things that could go wrong in the rebuilds alone.
A better fit for your needs might be a hard drive docking station. Otherwise, depending on how much storage space you need, one large or several large capacity hard drives sticking in place with a solid backup strategy might be your best bet.