Present progressive used out of politeness

[Winwin2011]

The followings are copied from Cambridge Grammar of English-A comprehensive
Guide:

Indirectness and politeness 341
The present progressive is often used to make a request, enquiry or statement of opinion more indirect, often out of politeness:

[a muffin is a kind of cake]
Are you wanting a muffin, Peter?
(less direct than ‘Do you want …?’)
I’m wondering when I could come and pick up the calendars that I ordered from you at the beginning of October.
(less direct than ‘I wonder when I could …’)
We’re hoping that it will have some practical benefits.
(lessdirect than ‘We hope that it …’)

In these cases, the past simple, and even more politely, the past progressive, may also be used with present time reference:

Did you want/were you wanting a muffin, Peter?
I wondered/was wondering when I could come and pick up the calendars that I ordered from you at the beginning of October.
We hoped/were hoping that it would have some practical benefits.
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I am wondering if the past simple and the past progressive used in the above context are more polite than using present progressive.

Thanks.

 

[bhaisahab]

"Are you wanting a muffin, Peter?" I don't find this very natural. I would say "Would you like a muffin, Peter?"