Each person can choose a mixin as high as they like when sending Monero.
For those that receive Monero solely from mining (never accepting Monero payments) is there any reason why a minimum mixin enforcement would be beneficial?
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For any particular person, maybe not. But in general, a miner might want to hide the fact that he or she may be mining (or even mining a particular block). For instance, if a third party knows you mined block B, and they see coinbase from block B moving, then they know it must be you.
The minimum mixin is imposed to prevent a tragedy of the commons scenario where people sending with mixin 0 would degrade the privacy of others who use (either before or after) those outputs as fake outputs. If outputs A, B, and C are used in a ring signature, then outputs A and B get spent with mixin 0, then C has no privacy added from the use of ring signatures.
The problem is described in https://lab.getmonero.org/pubs/MRL-0004.pdf, which recommends a minimum mixin value.
In short, having a transaction mix with others by default is important in keeping Monero anonymous. This is accomplished in two ways:
As user36303 described, privacy would be compromised if people you mixed with also did not mix their outputs.
It would be easier to search the blockchain for transactions that have mixins and separate them from those who do not. Then, criminals or agencies could target users who use mixins and ignore or devote less effort toward those who make not attempt to hide their transaction history. This is a similar issue that users of Tor face: they are often targeted for surveillance because it is easier to target just Tor users than the entire internet. If everyone used Tor, it would be harder to keep track of people. Monero privacy works in a similar way.