If it were a real motivation they could execute it much more effectively by not including their first-party app at all.

Doesn’t App Store utilization by both end users/consumers and perhaps more importantly developers, who make apps for end users, reflect indirectly in the share price?

If this were the case, the revenue to app developers in this instance could motivate Apple to not discourage this type of confusion.

I doubt leaving a BP app on there has any influence at all.

You're just restating the original point in a more convoluted way. Yes, Apple makes money from scams such as this. No, it's unlikely to be anywhere near the amount where it would matter, even in aggregate.

Do you think Apple had that 1 trillion dollars entry in their balance sheet spontaneously appear in one majestic swoop of same sale?