How can I tell Music for iPad to play all of an artist's songs without making a playlist?
Not obvious at all, but: 


Tap My Music from bottom nav.
Tap the red filter menu selection that's located roughly upper central on the screen, just below the Recently Added section. 


The filter menu should say Artists or Albums or Songs etc. Choose your desired filter option (Artists in this case). 
The list items below the filter will update. 

Tap the list item's avatar (tap the artist photo, in this case). Do not tap the list item's text (the artist's name), unless you want instead to navigate into sublists. 
A queue will begin playing from your selection. 


If you already had a queue, the old queue will be replaced with this new queue. 
The first song in the queue will not be random, even if you had shuffle enabled. 

An almost-too-skinny-to-tap bar will appear at the bottom of your screen. 


Tap it to view the current song, to access shuffle and continuous buttons, and to preview the queue (menu icon to the right of the fast-forward button). 

Complain to http://apple.com/feedback.