Whether spread should be considered as a cost or an edge/profit depends on your strategy.
Let's assume that the market is very liquid and the spread is always one tick wide.
A market taking strategy will buy at current best ask, and sell at future best bid, and that's one full spread (two half spreads) to pay. This ensures that orders are filled immediately with high probability.
A market making strategy will buy at current best bid, and sell at current/future best ask, and if both orders are hit, the strategy earns one full spread. Now it's quite uncertain whether your orders can be filled quickly.
Thus, you can think of the spread as the cost of takers paid to makers (liquidity provider) for immediate execution. As long as your strategy involves taking/crossing the book, then half spread has to be considered as a cost.
Also, relying on current book-weighted mid to calculate cost does not seem very reasonable to me. You can use it as a proxy of future price, but to calculate cost you should use price that will trade, since you are never gonna execute on mid price.
