Why do rechargeable batteries deplete so quickly compared to non-rechargeable?
The full chemistry-level explanation is beyond me, but the short consumer-level answer is to do with self-discharge. This is, as the name suggests, how much the battery discharges itself while not in use or in low-drain uses.

Some rechargeable batteries are marketed as "low self discharge" for these use cases. However, personally I wouldn't bother using rechargeables for anything with a life over six months because they have a finite shelf life anyway and are unlikely to see enough cycles to justify the extra cost.