Yes, I also thought it was a risky, maybe even naive, line up. Good for a home game where you dominate possession and it's all about finding ways to get through a deep defence. Especially as we got ahead through an early set piece goal, and then Birmingham were reduced to ten men. We didn't miss pace up front as there was no space to run into anyway. Birmingham had little to offer.
High on confidence, Wilder then spoke pre Wrexham about us wanting to control games, I assume wanting to dominate possession and press high, in most games. Thanks to Seriki's wing play and Bamford's goal nous we got two early goals. And we even got a third from McCallum's long throw.
From then on it was a very different scenario to the Brum game and it soon showed the team wasn't able to maintain the pre game tactics, nor adjust to the slightly unexpected scenario of being 3-1 ahead.
The starting line up relies on us attacking in numbers, playing on the front foot, pressing high, and creating chances when we win the ball. The team must remain compact, meaning the holding midfielders and back four must stay relatively high, and challenge aggressively if the opposition play through our first press.
At 3-1 away, these things become more difficult psychologically. The forwards' press become a little less intense. Defenders become reluctant to take risk and tend to drop deeper. When our high press didn't work, we became stretched, with gaps everywhere. Moore was tough to handle and they had many willing runners.
It may have been different with your suggested half time changes. With a threat in behind, you can be slightly less adventurous, leave some of the attacks to the forwards and maintain a more compact shape when attacks break down. Instead we did little to stop the game becoming too open. They kept going, found areas where we were vulnerable and punished us until the game had been turned completely around.