Public test environment only accomplish three things.
- Primarily allow Developers to test changes [i]without[/i] upsetting the existing balance of the live servers.
- Let Developers to get their feedback sooner.
- And for really impatient people to get to play the changes sooner.
The balance of the live servers is not so delicate that it needs to be "protected" by a public test environment, unlike a game like Overwatch which very much wants to be an e-sport. Altering a weapon's damage by 4% is not something you need a PTE for. Radical changes like alterations to the sandbox or redesigning Viking Funeral are more suited to having a PTE but these kinds of changes are rare.
There's also a matter of progression. Destiny is a game very much about what you have. It's inevitable that people will complain about stuff they have on the live servers not transferring to the PTE or vice versa.
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I disagree with your reasoning but a public test shard is an infeasibility regardless so it's a moot point. There is no practicable implementation possible within this game's prospective lifetime.