TLDR: I don’t have a lot of confidence that this will work out, but unless we make the attempt we won’t have the data to support that hunch. Plus until we do so, people will keep asking for it. But before we can, we would have to have some other stuff in place first.
Here are ELL migration stats:

That tell us that right now, almost one in every six questions currently migrated to ELL from ELU by moderators is being rejected.
For comparison, here are ELU migration stats:

Again, those are all moderator migrations because no one has a default off-topic migration path to ELU right now.
Perhaps for comparison, here are SO migration stats, where there are OT migrations available to regular close-voters:

The ones that are user-migrated are these:

There have historically been others, but they were removed because people were migrating too much crap.
Which is what I worry will happen with us.
The Historical Record
I once took a broad look at the ELU questions that had received comments to the effect that the post would do better on ELL.
My conclusion at that time was that if all those had turned into migrations, there would have been an overwhelmingly high rejection rate: not just a simple majority but maybe 80 or 90 percent.
It’s true that these were just comments not actual migration votes by 3k users with the close-vote privilege, so we don’t know what the votes might have been. And migration does require a super-majority of at least four out of five votes.
A lot of questions closed for General Reference or Proofreading on ELU that people say should be on ELL should not be, because they would just get closed for Dictionary or Proofreading there, too. That shows that people forget not to migrate crap, and are just looking for a dumping ground. That is a real problem.
We get plenty of migration rejections even now with only migrator-migrations. It could only get worse.
Due Diligence and Paired Reputation Requirements (not happening)
My gut feeling is that having CV privileges on ELU may not be a good enough qualification for making someone good at judging whether a question is a good fit for ELL.
What might work, but which is too hard because there is no code to support it right now, is for there to be a reputation requirement for both source and target site for migrations. However, the question asking for that, Require minimum reputation on the target site for migration, has been status-declined on MSE.
So unless and until this feature were reconsidered, it wouldn’t be possible to have a double reputation requirement. However, if it were, I wouldn’t mind starting with a requirement of Trusted User on both sites, and then consider halving it if that works out ok.
Yes, I know that’s very high. But I am afraid that at this point I quite honestly don’t have enough confidence that ELU-to-ELL migrations will be done well enough not to provoke bad feelings and high rejection rates.
What We Could Try Now
Based on the other ELU meta posts I linked to as Related in my comment on Rob’s question, I predict that the Community will come down firmly in favor of there being such a path.
If this is what the Community truly wants, or perhaps the Communities, then we could try it for a while.
If it works, it works.
And it doesn’t, then we’d have concrete data to that effect.
Even though this is my hunch, we don’t actually have that data yet, and can’t get it in any other way. It would cause no great lasting harm to give it a go for some initial trial period, whatever is long enough to acquire that data.
It’s going to take a lot user education first for there to be any hope of it working out well. We have over 400 users with vote-to-close privileges on ELU.
Just FAQ It
Therefore if we were to try this, we should absolutely have a FAQ here on Meta with concrete guidelines about just what should and should not be migrated to ELL, along with plenty of examples.