There are several - many - examples of failure to exercise power, and several examples of abuse of power.
Let's take the most obvious - and well publicized - example: Obamacare
We can talk about the lying, blackmail, and extortion it took to get the bill passed ... but that seems to be the political norm these days. Instead, let's just discuss implementation.
The Executive Branch does NOT have the discretion to change the law ... only to delay its implementation while contesting it in a court of law. Changes and waivers to application of the law - most blatantly, to favor political groups (labor unions, in the case of ACA or the Black Panthers in the case of voter intimidation, for example) - are not within his authority. However, once the courts have ruled on its constitutionality, they are REQUIRED to enforce it - whether they like it or not. Clearly, Obama overstepped his authority on the ACA and immigration issues.
Your argument about regulatory applications is specious ... and, frankly, non-applicable to this discussion. They are allowed to use regulations to dictate HOW they are going to implement a law, but they do not have the authority to CHANGE the criteria established in the law. History shows that one of the favorite ways for Congress to control an out-of-control executive branch is to establish specific performance criteria within the law, thus giving them no latitude whatsoever.
As for your 'abstention doctrine' reference, I'm not sure you understand its intent. It is only applicable when a court feels that hearing the case would interfere with the jurisdiction of another court - not whether the case has legal standing, but merely an issue of jurisdiction.
It is not a coincidence that, over the past two weeks, the current regime has begun to put the issue of impeachment on the table themselves. They are trying to convince the Republican base to push for the impeachment immediately. They well recognize that impeachment is coming, and their only hope to survive is to get it done before Harry Reid and the Democrats lose control of the Senate. They are not willing to gamble on a free and open impeachment trial.
