You already can achieve this: Delete your question, wait 40m, copy-and-paste it into a new question on another site.
I'm inclined to agree that it should be easier to do, probably at some kind of rep limit. If you've got 10k rep on one site, you probably get the general Stack Exchange format, you know that there are a such thing as the "help pages" and that they're actually informative, and you "know how to know" what is on-topic across the network. OTOH, there are much more pressing features, and it's not clear how much effort this would involve.
The argument against making this easy based on the premise of "users suck" could be used against literally any feature of the site: 'So few users get "asking a question" right, therefore, we need moderator intervention before questions can be posted.' If users are the enemy, stop letting them sign up for accounts. The formula to apply for this feature (and any feature) is:
user_value * users_affected * user_value_weight + (moderator_time_saved - moderator_time_spent) * moderator_time_weight - developer_time_spent * developer_time_weight
I suspect that moderator_time_spent
dealing with migration flags raised by the OP themselves is so low as to be negligible. Even if not, there almost surely exists some rep value so that, if the user has that rep anywhere on the network, they are more likely than not to make a correct judgement on a migration vote - this means moderators save time by having to deal with fewer question closures.
The moderator term is now >0, so we can focus on the user and developer. Others have pointed out that this will affect relatively few users. There have been several questions on this topic on Meta, though, and there are a lot of users with >2k rep on StackOverflow. Also, I sometimes leave comments on StackOverflow questions that the user might want to migrate to, say, Math.SE, so these sorts of comments might actually be acted upon if users could do so more easily.
That leaves the developer term. Other's have pointed out difficulties with account creation, so this is not a one-liner. I suspect that even if the value add here is "somewhat positive", the effort needed is large enough to outweigh it. Perhaps devs here can corroborate.