If many projects come to rely on InnerSource, doesn't that mean that it is successful?

That would be my definition of success, yes. But then, I'm not a manager. The benefits of InnerSource can sometimes be hard to quantify, especially the soft factors, such as employee satisfaction, improved learning and increased networking. Not being able to put hard numbers on e. g. the increase in efficiency might make InnerSource look like a failure to some managers.

Would a decision to shut it down then be very unlikely?

I think there are shades of grey, here. If the company does not support InnerSource on the highest level anymore (e. g. no funding for central platform), the projects which are relying on InnerSource would most likely maintain a more islolated version of it for their particular use. I guess you could call that InnerSource, too, but it would probably be a step back from the values of openness and transparency.

Does this force represent a fear that management has about even starting this (a worry that they would lose control over the program because of its popularity)?

Yes!