I think people rely too much on "higher limits beget higher limits" and such. In general, when we're talking about a computer reviewing applications, it's looking at your scores, income, and payment history, not really your other accounts/limits. Yes, it is seeing if your history is in good standing, but I doubt that it's really analyzing to the extent of trying to "compete" with your other cards, especially because every lender has different criteria for limits.
On a manual review, it's possible that lenders can view your other limits and be willing to be more generous but this is a case by case basis. Once you display responsible credit use, build up a history, and have a solid income, you should have no issue getting the limits that will be perfectly sufficient for your spend.
