Recall that the WACC analysis is meant to capture the MARGINAL cost of capital for the company. As such, you definitely use MARKET VALUE of equity and debt.
In reality, for non-distressed companies, we proxy market value of debt by using book value of debt. Minor, immaterial differences, so no worries.
However, book value of equity is NEVER appropriate for WACC because you don't issue new equity valued based on shareholders' equity (book value), but instead, on the current market conditions. As such, were the stock to tank, and the company issues new equity at that time, (just think back to banks back in the credit crisis), then, yes, they'd be doing it at the worst time. The cost of equity would then rise since clearly the premium required for investors to invest has gone up (by simple virtue of the fact that prices dropped).
Also, we don't think that Shareholders' Equity is intuitively the "actual capital structure of the company" as you noted. Shareholders' Equity is an accounting term fraught with accrual concept of accounting issues. At day one of the company's IPO, it is the actual capital structure. But after that, it's not.
Now, our question to you is the flip opposite - if the stock rose dramatically instead of tanking, would you have the same question? Or you wouldn't have bothered asking this question because "stock prices generally rise not fall" (which is complete BS). The opposite scenario to your question is also true - and that is why companies like to issue more stock when prices are high because you can sell more stock and give up less ownership percentage.
If the price takes a huge hit, the proportion of equity to total cap would decrease, yes. But then the cost of equity capital in theory goes up. Two-way street!
Side Note: when calculating beta, specifically unlevering and then re-levering your competitors' betas for CAPM, the Hermada beta equation uses book value of equity and debt (not market values). This makes sense and isn't mixing apples and oranges because the variability to profits is based on ROE (book value of equity). Refer back to our Corporate Valuation slide materials in comparing Company A (unlevered) with Company B (levered).