Why isn't CoinJoin implemented as part of the Bitcoin software, and mining process?

If I understand correctly CoinJoin/CoinShuffle, it is done by combining and mixing inputs and outputs from several transactions so that it is harder to identify the origin of those transactions.

Could this process be implemented as part of the Bitcoin software itself? So that when a new block is mined all inputs and outputs in all the transactions included in that block are mixed (CoinJoined), thus making Bitcoin more private?

It even sounds like this change could be implemented as a soft fork, backwards compatible with old rules?

Sorry if this is completely stupid and makes no sense at all, or if it is already in some BIP that I could not find.

submitted by /u/throwawaybtcstupid
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