Systems from this era were probably using BCD rather than base-10 strings. A BCD date would take up 24 bits.
Running a complicated date routine to convert to/from 32-bit timestamps would also have cost a huge amount. These machines had speeds measured in thousands of operations per second, and the division operations needed to do that sort of date work would take ages, relatively speaking. All on a machine that cost dozens of times the average yearly wage at the time, and accordingly needed to get as much work done as possible in order to earn its keep.
Running a complicated date routine to convert to/from 32-bit timestamps would also have cost a huge amount. These machines had speeds measured in thousands of operations per second, and the division operations needed to do that sort of date work would take ages, relatively speaking. All on a machine that cost dozens of times the average yearly wage at the time, and accordingly needed to get as much work done as possible in order to earn its keep.