The simple answer is that they just didn't need them! Why reinvent the wheel, when the required interface is already provided by the ROM BIOS? This allows the operating system to be more portable and to support a wider variety of machines and hardware from different vendors, because the vendor provides and is responsible for the ROM BIOS routines. Size of the OS itself was also certainly a consideration, as you rightfully point out.
The converse question is, then, why do modern operating systems have their own drivers to access hardware? And the answer to that is rather simple, too: because they have to! The ROM BIOS routines are designed to be called from real mode, but modern operating systems don't run in real mode. Instead, they run in protected mode (32-bit) or long mode (64-bit). Since the ROM BIOS services are unavailable from these modes, the operating systems must provide their own drivers. The ROM BIOS services are often still used, even by modern operating systems, during the boot-up phase before they switch into protected/long mode. (All x86 processors boot in real mode, compatible with an 8088, even to this day.*)
* Except that, as of the Intel Haswell microarchitecture, the A20 gate is no longer supported.