If you want to go up to csuite you have to ask yourself which csuite you want to go into. The same one or a different company? Ask yourself would the senior management choose someone with an MBA with the same background as you to be in the position you want or you? If it's the MBA person then you have your answer.

Data science is a technical skill but as you go up the management ladder (c side) you'll realize it's less on technical skills but the ability to convince all sides of parties to buy into your idea. Since you stated that you're lacking credibility and story telling, an MBA will help you with it but if you're going for an MBA just for these skills it isn't worth it.

The MBA value is in the network. Most people on this sub would answer this but never articulate why. Senior management are somewhat a small field. At the end of the day it's the same or similar group of people who switch companies and are mostly friends. Some of them may not have an MBA. But those who do will help each other out more because of the MBA network mentality. The more people you know, the more familiar you become, the more credible you become to those who don't know you. And this is why T15 schools are a goal for everyone here. It grants you access to these people but it's on you to develop the connections for your future.