ESP8266 uses an external NOR flash, it’s not a EEPROM. The write cycle is about 100K (not 10K). Also, the write cycle limit is for each sector, not the entire flash at once. That means, if you repeatedly write into the same sector 100K times, then that sector may approach the end of its life. Log files are written into different sectors each day. The firmware will erase old files when it runs out of flash memory space, which means it will take a long time (months, years) to come to the same sector again.