I don't think your summation is accurate at all. LA, Boston, San Antonio, Miami and the previous LA incarnation did not win with depth. In fact, I wouldn't even say Detroit won with "depth." Detroit didn't win with the best 1-2 players, but they absolutely rode their fantastic starting five.
All of those teams won primarily by riding their starters hard. They all had some players off the bench, but not excellent players. They had the types of players you can get with decent drafting at the end of the first round and in the second round and/or wise uses of the MLE or even LLE. None of them were fielding a second unit of players who could start on some teams.
Portland needs some players who won't completely embarrass themselves, but they don't need high-level players (starter-quality or near-starter quality) like Fernandez, Outlaw and Przybilla on the bench. Most of the players that get lionized as "great reserves on championship teams" are actually pretty ordinary players that can be counted on to do a few things when defenses are focused on the superstars. They often then get overpaid or given too large a role on non-descript teams, due to having been shown to "winning role-players," and prove to be nothing special.
So, sure, you need an Eddie House or past-his-prime Jason Williams...you don't need a Rudy Fernandez. A Rudy Fernandez off the bench certainly is nice, but it's less valuable than an improved starting unit.