I don't know if we were absolutely the deepest team prior to the Gallinari and RWill injuries but I agree with ESPN that we were "arguably" the deepest (it is somewhat subjective at best) and certainly deep enough to make another long play off run. But now we aren't.
I think if we were to add Whiteside or Cousins, we would be deep enough again, at least once RWill is back. Until RWill is back, we are deep enough to get by (a lot will depend on Vonleh).
Smart White Pritchard
Brown Brogdon Thomas(?)
Tatum Hauser Jackson(?)
Horford GWill Vonleh
RWill Whiteside Kornet
To me the soft spot is back up SF. That is a stretch for Hauser but he can really shoot. Pritchard may end up playing more than Hauser so this isn't necessarily a problem, at least not until someone gets hurt.
If the benchmark is for a team to be deep enough to lose 2 of their top 4 bigs (1 starter and 1 core bench) and not suffer from it, that seems like a pretty unrealistically high bar. We were plenty deep before the injuries, "arguably" the deepest team in the league. Not sure how you can be critical of an off season where we added 2 stellar bench pieces (Brogdon and Gallinari) to one of the best core rotations in the league.