The folks I met who were talking about AI Safety in 2018 were certainly sincere, and the two people I knew who later joined Anthropic seem like the type to do it for the greater good instead of money.
I expect that Anthropic will eventually behave as you describe, like any other public corporation. However, my impression is that its current leaders are still more sincere than greedy.
Unfortunately, money changes people. 2018 was a long time ago. Before AI was considered a product you could really market in the current sense. Before trillion-dollar valuations became a prospect.
Remember how OpenAI was supposed to make open-source models and cap its potential returns to investors at some multiple of their principal (my memory says 100x, maybe I'm wrong)? Well, that went out the window as soon as the word "trillion" was mentioned.