The M1 won't, the SSD will wear out before that and with no way to swap, it will be landfill as well.
If the characteristics of the SSD in an M1 are sufficiently similar to the SSDs that were used back then (I have no clue if that's the case), wear out will be a non-issue.
This is why people are concerned about SSD endurance. An old SLC SSD's NAND would be good for many, many writes, tho the controller would often fail. Nowadays the NAND fails, but the controller is fine.