The reason the examples in OP of 'just do...' irk is because the 'just do...' supposes to be helpful, but any sincere thought given shows that the suggestion isn't helpful.
Instead of giving sympathy/relatedness, it comes across as dismissing the problem. -- I think this can be down to miscommunication; but I think whether something 'sympathises with problem' or 'gives solution' is deeper than a phrasing.
The message is not the meta-message.
The reason the examples in OP of 'just do...' irk is because the 'just do...' supposes to be helpful, but any sincere thought given shows that the suggestion isn't helpful.
Instead of giving sympathy/relatedness, it comes across as dismissing the problem. -- I think this can be down to miscommunication; but I think whether something 'sympathises with problem' or 'gives solution' is deeper than a phrasing.