If the banks cared they would provide either token-based API like oAuth or at the very least, a read-only password for users to give these sites that aren't fully credentialed. Customers will always want to extract their data.
It's absolutely true that offering data migration services decreases bank account stickiness, and that's something everyone is terrified of doing in the finance industry. Customer acquisition costs are so high, I doubt you'd believe me if I explained them to you.