How can I claim most managers mainly using digital tools for productivity-reasons?

Here is an answer.

Well, I have not done statistically proof-based research on this matter, so of course there is a limit on what I can claim. However, you might be interested of finding your own answer to this question. If so, then try this with a top management-team (I myself have tried it fairly lot):

Ask the top managers to create just a rough list of all “digital” projects they run in the organization at this moment. When the list is made ask them to mark these projects according the following three categories:

1. Projects they do in order to make something faster/cheaper, to make a process more stable/faster and/or in order to increase quality.

2. Projects they do in order to make customers more happy than they already are.

3. Projects they do in order to prepare for a fundamentally new business landscape.

My experience tell that the majority of projects end up in the first category.

But it is better that you develop your own opinion. It actually does not matter what I believe. What matter is what you believe.