If you were to ask what single aspect of improvisation is missed on young improvisers I would with out a doubt answer the poetry of the music. That, to me, is what separates great soloists form the rest of the pack. Focusing on note choice alone will never get an improviser to master forms and truly be able to express on a profound level.
The blues is a sound, its a form, its a style, but more than any of that it is a poetic structure as universal as Haiku, or limerick or even sonnet. Lets look at one of the masters, Langston Hughes:
But if you were to ask me, how the blues came to be
Say, if you were to ask me, how the blues came to be
You wouldn't need to ask me, just look at me and see
This is the standard formula for the poetry of the blues. Three lines, the first two lines relatively similar, and a contrasting third line. This doesn't mean that every time someone solos that this structure has to be followed perfectly. There are many ways that this can be flexed and adapted. However, this is as important to teach young improvisers as anything else. It begins to set an organization for solos that can be applied to a variety of forms. It teaches confidence through repetition. It encourages the development of musical ideas that are repeatable. It sets the discussion for phrasing as well as form in motion!
A great resource that shows how poets use the form as well as flex the form is Blues Poems by Kevin Young. This anthology includes both poems that follow the above structure verbatim, as well as poems that push its boundaries. I think creating a connection between the music and the poetry of the form is a vital aspect of this tradition.
There are some really good examples of this kind of poetry in improvised solos. Harry Sweet's Edison on St. Louis Blues, Joshua Redman on Jig a Jug, Sonny Rollins on Tenor Madness all have elements of this poetry - and that is but a small sampling. The take away here is this - the really master this style, we have to do more than play right notes. Dig into the poetry, the lyriscim of what this music is expressing and be intentional about how those formulas can apply to your playing.