Early PC towers often used such a design, if only because they were basically desktop PCs on their side. Some systems even had a rotatable drive bay (a bay containing two full-height 5.25” emplacements is as high as it is wide).
There were some systems specifically designed along the lines you mention; Apple’s Quadra 950 and PowerMac 8100 spring to mind, and in less common systems, Digital’s Personal Workstations are nice specimens.
In the PC space though, the design wasn’t all that popular, at least when using standard components, because of motherboard constraints, and of target markets. Regarding the former, Baby AT systems did commonly put the hard drives and 3.5” floppy drive alongside the motherboard; but the number and size of expansion cards limited the ability to reduce the case’s size, and giving users access to memory slots etc. meant either having to develop specific “easy access” drive mounts, or leaving the case large enough to allow hands to fit without getting too badly torn to shreds. See this photo for a typical example of a baby AT clone. (Baby AT motherboards were really long too, so reducing the depth wasn’t possible anyway.) Regarding the latter, in the nineties most people wanted desktop systems, and towers were sold based on their enhanced expansion possibilities; reducing their size wasn’t part of the specification, on the contrary — the bigger the tower, the more serious the system, in many people’s minds (and on magazine covers).
ATX and related standards didn’t improve things much in terms of size reduction; the main consideration in the design was airflow. The same was true of BTX. The standards call for a fair amount of clearance above the motherboard, especially around the CPU — bear in mind that PCs in the early 2000s used slotted CPUs, not socketed; and while the Pentium 4 moved back to sockets it brought with it huge cooling requirements — so that combined with the expansion card requirements and easy access to memory means that designing a system with the motherboard behind everything is rather complex. (Not that it can’t be done, some small systems do exist, but they typically rely on specific equipment — low-profile CPU coolers, low-profile expansion cards if any, no 5.25” devices...)
The decline in popularity of 5.25” devices means that they are no longer a design constraint; but general purpose side-by-side designs still tend to follow the “humongous tower” approach. See Lian Li’s PC-011 for one example of a system with no 5.25” bays, or their PC-D600 and PC-08 for two-compartment designs with 5.25” bays (this type of case has been around for decades).
In summary, yes there were some towers with motherboards on a back plane behind everything else, but they came with constraints:
- complicated access to devices on the motherboard;
- limited airflow;
- limited expansion capabilities (which ended up being rather ironic for a tower).