Yes, rerolling initiative each round without making action declarations first works, in the sense of being a functional way to play the game. It works well enough that it's the standard approach in many non-D&D RPGs.
No, rerolling initiative each round will not prevent the kind of coordination described in the question. Even if the initiative order changes from one round to the next, the order for the current turn is known (or at least can be known) when each person takes their turn. The players may not know "we both go before the goblin every round", but they still do know "we both go before the goblin this round".
If you want to prevent that kind of coordination (which may or may not be appropriate, depending on your characters, preferred style of play, etc.), you need to have the players decide what to do before they know whether they're going to act before or after the goblin this round, which is the purpose of doing action declarations before rolling initiative.
To expand on the "or at least can be known" comment, one way of dealing with dynamic initiative systems is to do an initiative countdown each round. e.g., The GM might say, "Does anyone have an initiative 25 or higher? No? 24... 23...", then Alice says, "I have 23" and takes her turn. When she's done, the GM asks, "Anyone else on 23? 22... 21..." and so on. When using this method, it's common for nobody (even the GM) to know the full initiative order at any given time, although you could still announce your initiative position if you want others to know it, or ask them for theirs before the countdown reaches them.