Q:

Why use ultra-wide with short focus?

I have a Samyang F/2.0 12 mm for the Sony E Mount, so the 35-mm equivalent focal length is 18 mm (crop sensor 1.5×).  I use it mainly for landscapes and architecture in order to fit more in my frame than I can with my other lens, usually focussing close to infinity (I also use it for photography of starry nights such as the milky way or star trails, as it is also by far my fastest lens).  I sometimes use it in small indoor spaces, with a focus perhaps down to 1–2 metre at the lowest.  But I've never used the lower half of the focus ring, which includes focus down to 20 cm.  When I want detail, I tend to use my zoomlens (18–200 mm).  Under what circumstances would one use a wide angle lens with a focus less than (say) 50 cm?
In the example below I took different photos of the same object, first twice with my Samyang 12 mm prime lense, then three times with my Sony E 18-200mm zoom lens, at various object and focal distances.  I downsampled the images from 4000 to 1200 pixels wide but otherwise did not do any other post-processing than in-camera processing.  The candle holder is about 9 cm high and 12 cm wide.
To me, the photos with the zoom lens appear more interesting for this purpose.  The bokeh is stronger (even though all photos were taken at F/8.0) and the object fills more of the frame.  What possibilities does an ultra-wide lens offer when I focus on an object that is close by?
Samyang 12 mm

12 mm (35-mm equivalent 18 mm), 20 cm distant

12 mm (35-mm equivalent 18 mm), 30 cm distant
Sony E 18–200 mm

18 mm (35-mm equivalent 27 mm), I think 20 cm distant (not sure)

48 mm (35-mm equivalent 72 mm), I think 40 cm distant (not sure)

146 mm (35-mm equivalent 219 mm), I think I was about 1 metre distant (not sure)

A:

A very good way of using an ultra wide lens is to get really close and get something right in the viewers face. Using a wide angle lens to get everything in the frame often leads to very boring pictures because the viewer has no idea what the photo is about. 
Ken Rockwell has written a very interesting article about his:
https://kenrockwell.com/tech/how-to-use-ultra-wide-lenses.htm 
Digital Photo mentor also wrote an article about how to use wide angle lenses:
https://www.digitalphotomentor.com/5-mistakes-beginners-make-using-a-wide-angle-lens-and-how-to-avoid-them/ 
This article from Photography life 'focuses' mostly on landscape photography with wide angle lenses:
https://photographylife.com/how-to-use-wide-angle-lenses
To get a close-up of something with a wide angle lens, you need to get extremely close. Everything seems about 3 times further away in the picture due to the focal length, so you need to get much closer than 50 cm to get something really close. 
You would probably wish your lens could focus a bit closer than 20 cm if you want to make a picture like this:
https://flic.kr/p/3Paa94

A:

The distortion of wide angle lenses allows you to magnify the subject relative to the rest of the frame, leading to dramatic or otherwise interesting compositions.
Doing a close-up allows you to use perspective to further exaggerate the relative sizes. The wide angle also allows you to include more context than a telephoto lens, especially at close range to the subject.
Here's an example from Outdoor Photographer, photography (c) by Rob Sheppard. Note how the features of the tree in the foreground are highlighted, but are also set in the context of the mountains in the background:

A:

As @Agent_L says in the comments, if you take photos with your 2 lenses at exactly the same short distance from something, the answer to your question becomes more obvious. If you are curious about this - and you must be, since you asked here - then you should simply take the photos and see for yourself.
Different lenses are useful in different situations. Next time you are out in a forest or field, and come across an enormous mushroom, take a photo from 20cm distance using your 2 lenses, see the effect of the result, and the reason why someone might choose a close-up, wide-angle shot becomes self-evident.

