

Probably many greedy reasons, but my personal favourite speculation: annexing Greenland surrounds Canada and stops any potential aid by its NATO allies in case of an invasion, since annexing Canada is one of the stated objectives of the US now.
In terms of strategy for actual national security, they already got all the access they wanted, if they wanted more all they had to do was ask. If they’re the ones doing the attacking of a common ally, though, they wouldn’t get that access. So it’s only of added strategic value to annex instead of maintaining the alliance if the goal is to attack members of the alliance.
The central command is there, but it’s led by America. This means that, if we rely on NATO mechanisms, America effectively controls collective responses by Europe, which is undesirable now that they are not on Europe’s side in the conflict with Russia, and they state over and over again that they intend to annex Greenland.
A European central command and standardisation between countries makes a lot of sense to me. If member states don’t want to give up autonomy, maybe with some kind of opt-out clause. That way the countries that are willing won’t need to coordinate poorly through dozens of bilateral communication channels, but can jointly operate with a common strategy, and at worst, not all member states would contribute to every action. Plenty of possibilities for problems still, but a step up from the current situation.
I would personally still prefer to see a more integrated European military, though. While we will have a bunch of low-population countries all doing all possible tasks poorly, instead of having some specialise to specific strengths and sourcing collectively, the EU will always be weaker militarily than a comparable force that is not split in such a manner.