Hi Dave, and welcome to the forum!
You ask an excellent question - one that I have asked myself and have been giving some thought to.
The SBCK seems to work pretty good for constructing solos in a formulaic "planned" manner, but my personal ultimate objective with the course is to achieve exactly what you suggest. To be able to construct solos "on the fly" in real time, to the point that a person could play somewhat endlessly over a long backing track without repeating the same stuff over and over again, or at least not in the same order, and in any key.
The exact method to achieve that is probably somewhat different for everyone, and I am not yet certain exactly what will work for me, much less someone else, so all I can offer is my train of thought and speculation.
In a pretty general sense, I do believe that one prerequisite involves acquiring a fairly large vocabulary of licks, and variations of those licks, such that they can be played without any thought or concentrated effort, and recalled without hesitation so that they just flow from the fingers. This is a pretty tall order all by itself that will take me quite a bit of time and practice - possibly years. I'm a slow learner.
But I don't give up easy.
The next step is to be able to "hear ahead" at the same time you are playing, in order to hear and select what will sound good against the backing track (or a live ensemble), and do this fast enough to be ready to play it when the time is right, while then hearing and selecting the next part to play, and so on and so on until they pull the plug on your amp and kick you off the stage.
The next step in the progression would be to be able to play melodic lines simultaneously as you hear them in your head, or with just a very short delay. In other word, your finger just (magically) play what you are hearing in your head in approximate real time.
I find that there are some magic moments when I am actually able to do these things just described, but usually not for very long, and not very consistently. Even these occasional short episodes (accidents??) of brilliance (LOL) are enough to encourage me that my goal is ultimately achievable, if I live long enough.
If there is one word that sums up everything needed to reach the objective, I think it would be "fluency".
This is probably of absolutely no help to you, but writing it down helps me commit to it.
Time's a'wasting - better get to it.
Later,
Tom
Also, I forgot to mention, that in my opinion, until one has acquired pretty good fundamental playing techniques, the above objectives will be much harder / slower to achieve. There are so many moving parts happening so quickly, you can't be thinking about executing basic technique at the same time. Lots of things need to happen without any thought so that the mind has time to think about what's really important. When you watch a really good player, he or she makes it look effortless - because to that person, it is virtually effortless - they have reached that level of fluency.