Zook had four huge recruiting classes that altered the talent level of the program. 06, 07, 08 and 09. Beckman inherited a bunch of great seniors from that last class - Buchanan, Spence & Hawthorne chief among them - and made a total mess of his first season.
But beyond that little overhang that ended up being meaningless, Lovie's inheritance was no worse than Beckman's or Zook's. None good, but none hopeless either. Nor will, barring disaster, our next coach inherit a Kansas-type situation.
This "write off 2-3 seasons" thing that has become fashionable as excuse-making for a new coach is nonsense. It takes time to win consistently. It does not take more than a year or so to compete and demonstrate clear improvement.
I would say the inheritance that Zook got was significantly better and Beckman's inheritance was slightly better even if you discount those 2012 seniors. That said it was the cloud that was left over the program from Beckman and the timing of Lovie's hiring put him at a bigger disadvantage than his predecessors.