Can you blame a company for prioritizing people who have worked in similar environments before?
In large corporations technical responsibility is often more distributed than in startups just due to size, so your technical skills, while important, are typically less important than they would be in small-business/startup land. What fills in the gap is communication skills and your ability to navigate corporate social networks. If you can't conflict resolve issues between engineering teams, well guess what? That engineering team you can't work with is going to hold you up and cost the company money while your superior, who really has better things to do, has to take time out of their day to address the issue you should have been able to handle.
Not saying it should be a mandatory skill, but you can't blame large corporations for filtering for it. It's a factor.
Most companies smaller than multinationals are still large enough to have conflicts between teams. The most common failure mode I see is people who simply opt out of those conflicts, preferring to keep their heads down and write code rather than talking about what should be done and how. I'm not familiar with how it works in older companies like IBM, but at the FAANGs of the world, participating in those discussions is what distinguishes entry-level engineers from more senior ones.
If your experience is only in companies with a handful engineers, yes, it can unfortunately be pretty hard to get a senior position at larger companies. It's not impossible, but people will have justified worries about whether you can handle the responsibilities.
In large corporations technical responsibility is often more distributed than in startups just due to size, so your technical skills, while important, are typically less important than they would be in small-business/startup land. What fills in the gap is communication skills and your ability to navigate corporate social networks. If you can't conflict resolve issues between engineering teams, well guess what? That engineering team you can't work with is going to hold you up and cost the company money while your superior, who really has better things to do, has to take time out of their day to address the issue you should have been able to handle.
Not saying it should be a mandatory skill, but you can't blame large corporations for filtering for it. It's a factor.