Why should the non-important activities be done at all?

If I delegate something urgent and non-important to another, doesn’t that:

1. Urgently interrupt someone else?

2. Set them up to urgently ask me questions about something unimportant.

3. Burn some of their trust in me when they complete it and I’m not grateful.

?

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It seems the bottom two should be:

Urgent & Not Important: Drop

Non Urgent & Not Important: Maybe Play