Most likely the key is simply worn, and the lock barrel is not worn out. They were designed to wear the brass plated key, and not the lock.
A new key copy will be better, but a new key cut from the lock code will be like new. Original keys have a 4-digit code on them, which may also be stamped on the ignition switch. A superb locksmith can recreated the code without the code number, just by examining the key.
Your 1000 has a dashboard-mounted ignition switch, not a column-lock unit, right?
1200 STD ignition switch
(1000 switch is similar, but with different key shape)
Nissan part numbers for Datsun 1000:
* 25150-10600 COMP.-SWITCH, ignition & starter ALL (ex. Coupe)
* 25150-80001 COMP.-SWITCH, ignition & starter ALL (ex. Coupe)
- from C/# B10-017001, VB10-016001
* 25150-H0100 COMP.-SWITCH, ignition & starter (op.) ALL (ex. Coupe)
* 25150-25700 COMP.-SWITCH, ignition & starter Coupe
* 25150-H0300 COMP.-SWITCH, ignition & starter (op.) Coupe