I make no judgment as to the outcome and believe the OP when he or she says that everyone had a good time with it. I still think the assent to roll initiative in this case is worth examining.
Haha, yeah I was aware in moment that it was a judgement call as to whether to assent to their request for Initiative. But I happily decided on "Okay, Yes", because:
1) there have been a few other times in our campaign when the players themselves have asked if they could go into, or stay in, Initiative mode outside of combat, so that everyone could take their turn (in talking or making skill checks) in an orderly fashion. And so, it was not a novel or anomalous ruling to allow (call for) Initiative in what was not necessarily a combat encounter...but which certainly *appeared* to be a combat encounter to the players.
And 2), it would be a bit of fun. Anyway, the players were satisfied. They are still proud they so roundly defeated the Bronze Statue. It's not like I made fun of them (except on this ENWorld thread! haha)
Even if it were clear to everyone that it was just an Object, such as the broad side of a barn (or a dread gazebo), if two or more PCs are kinda competing to see who hits the barn or gazebo first, then let's roll Initiative!
Following the previous fight with the Living Rock Statue, they had clearly dropped out of the previous Initiative, having regrouped themselves into marching order to walk down the hall. And their blitz approach to the second statue was not that different from their blitz approach to the previous statue. The only difference being that I told them the Living Rock Statue had started to move, at which point I'd asked for Initiative. Yet as they approached the second statue, I told them that the statue was not moving. Yet they were still set on preemptively wailing on it, just in case it turned out to be animated. So, if they're going to take turns in melee attacks on an Object, let's roll Initiative! And it really mattered who went first, because the first person to hit the Bronze Statue with a metal melee weapon would receive an electric shock. (Yes, that was all in the BD&D adventure-as-written.)
The Initiative question is a separate matter - and I know it was a fine ruling, though understand it could've been ruled in other valid ways, as other posters have voiced.
The question of targeting an Object with a magic missile would've still been there even if they'd stayed in Initiative order following the previous encounter.
The two issues are only related because they both relate to whether and when the players can know, in a meta-gaming way, whether an entity is an Object or Creature (in the case of targeting Magic Missile) or whether the entity represents a Non-Combat Encounter or Combat Encounter (in regard to whether Initiative is called for).
My question wasn't whether the "presence or absence of a call to roll Initiative" can be used by the players to determine whether an encounter is a "combat" or "non-combat" encounter. haha