The uncertainty principle does add a pretty decent reason behind why we cannot reach absolute zero, leading to zero-point energy.
However, we can use thermodynamic arguments with entropy and the third-law to show that any closed system cannot reach zero by any procedure in a finite number of finite operations. This is kind of a macro-level explanation really as opposed to the QM level explanation, but they’re essentially equivalent.
There’s probably some level of explanation towards this in QFT too, ie quantum foam.
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