As some of the greybeards have suggested, a ballpark knowledge of the gauge numbers is enough to get the crew out of trouble for the majority of failures.
Main problem I see is that, unless the pilot either handflies enough (or, at least, follows what the automatics are doing routinely in an intelligent monitoring way) s/he is not going to have that facility when the gremlins set the scene for excitement as they do from time to time.
It's not difficult .. only requires some repetitious directed exposure/practice.
Similarly to Parabellum's sim example, I used to get the cadet level first endorsement trainee progressively up to the point where s/he could fly a single pilot low vis circuit with all the PS instruments progressively failed (or covered) during the takeoff. The aim was to keep it under a reasonable semblance of control, find the ILS and execute a safe landing recovery in min vis conditions.
Not looking for any great finesse .. just a workmanlike, successful result. Main aim of the exercise was a confidence builder but it reinforced to the trainee that one actually can recover the aircraft with a lot of stuff not working .. just takes a bit of thinking and keeping calm while one puts the acquired basic flying skillset into practice.
In the real world, naturally, one doesn't do that sort of thing, other than in extremis, and the two crew recovery with the aid of the QRH is the rule - usually for a simple failure situation. One uses everything available to assist resolution of the problem.
However, it is useful to the pilot to know that it can be done if the wx conditions aren't too severe.
I really can't see why a simple failure such as loss of the ASI should be cause for major panic for a well-trained, intelligent pilot. Even if the instrument is giving obviously duff gen, it is a simple matter to cover it so that the output doesn't confuse/complicate the pilot's cognition process.