> Wouldn't it actually just deter companies interested in acquiring out of interest 
   > in the acquisition's customer data?

Yes, that is exactly it. So at some level the data is a company asset that has 'value' to a potential acquiring company. And if you decide to destroy the value of that asset to an acquiring company (by having it self destruct on acquisition) then you've intentionally reduced the value of the company. Your fiduciary responsibility as a board member or executive is to maximize the value of the company.

The long held theory here is that the share holder's elect board members to represent their interest in the company, which is notionally the 'value' of their shares, so for the board to be doing the shareholder's bidding they would not allow the CEO to explicitly damage the value of the company by impairing one of its assets with a destruct clause.

I think it could be more nuanced than that. You could trade that possible future value for good PR and public image, especially if you are fighting a lot of bad PR because of people's worries about that data. Putting a clause in without letting anyone know about it would be destroying the value, but if you attempt to capitalize the on public perception of the move I think it would be really hard to make a case that it was irresponsible without some corroborating evidence that nobody thought it would help.

That seems like a dubious analysis. If the destruct clause helps sales, then maybe its not irresponsible after all.

By this logic, having a sale is also a violation of fiduciary responsibility.

As others have pointed out, looking only at the costs associated with a decision to "spend" assets is not what fiduciary responsibility requires.

At an implementation level, you could make it optional for customers to delete their data (preferably opt-out of deletion).

A purchaser looking to woo your clients (and continue to provide your service) rather than exploit your goodwill shouldn't have trouble retaining the majority of the data.

There's no reason to force data deletion, but leaving the choice to customers if they want to trust the purchasing company the way they trusted you prevents a lot of conflicts of interest and abusive behaviors.