Objective list of things Blizzard would need to do to release Legacy servers.
** Either update the current client to work with Legacy servers or grab a copy of the Vanilla client and update it to work with the Battle.net launcher**
Both of these have cons. If they use the current client, that means that they'd need to update all of the Vanilla client files to work with the new file format. Since WOD they've moved away from using .MPQs. Blizzard would need to work all of the Vanilla assets into the new file format.
Also of note would be that this would increase the download and install size of the client on every users' system, regardless of which servers they played on. This means bigger downloads for people with capped internet, slow internet, etc. It also means that when Blizzard patches Legacy servers, Retail WoW users have to download the patch to play. When Blizzard patches Retail, Legacy users have to download that patch.
Splitting the client and using one client for each means that Blizzard needs to update the Vanilla client to work within the Battle.net launcher. It also means that work needs to be done on the Vanilla client to handle all non-game related software updates. All security updates, system updates, warden updates, etc. would need to be updated to work with both clients. Every single time Blizzard updated one client with a security fix, they'd need to literally code it for both. This forking of codebases is probably the #1 no-no with software engineering and is avoided at all costs.
** Get the Vanilla wow servers to run within Battle.net **
Because Blizzard would be handling credit cards, addresses, real names, and other PII they'd be responsible for the security and maintenance of customer privacy and information. They'd be liable if any of this information were leaked, potentially receiving lawsuits from banks should credit card numbers be stolen.
Obviously they have their security system in place under Battle.net (all games that use credit cards run through this, as well as the purchasing of games that do not) so they'd likely just reuse that. This means getting the Vanilla servers to run within the Battle.net environment. I have no idea how much of an undertaking there is involved but I imagine that their server code, libraries, architecture and the like has changed quite drastically in the past 10 years. Think about all of the security that has been broken since 2006. All of that needs to be replaced and fixed. WoW's code is so spaghetti that they can't even increase the bag slots. I can only imagine the headache involved with trying to fix the security.
One thing to note is that private servers more than likely don't bother with this since most use PayPal or something other than Credit Cards.