I agree with most of that, especially the part about traveling to a location closer to the border.
However, most credit cards will not reimburse the global entry application fee. The list is somewhat small in fact.
https://upgradedpoints.com/credit-cards/best-credit-cards-for-global-entry-credit/
There's none I could find with no annual fee. The cheapest one has $45 annual fee. Although if one was already planning on getting one of these cards, or already had them, then it works great.