Valuing equity of a firm using WACC gives incorrect results

Suppose I have a free cash flow to the firm FCFF and the market cap is E. Obviously I don't believe the equity valuation and that's why I would even attempt valuating it. So one way to do it is find WACC

$$ R_{WACC} = \frac{E}{E+D} r_E + \frac{D}{D+E}(1-t) r_D $$

and value the equity as

$$ \tilde E = \frac{FCFF}{R_{WACC}} - D \tag{WACC method} $$

However, a more direct way is to evaluate the free cash flow to equity FCFE

$$ FCFE=FCFF - r_D D (1-t) $$

and use this directly

$$ \hat E=\frac{FCFE}{r_E} \tag{Direct Method} $$

Now the point is that in general the two valuations will NOT agree unless we have $E=\hat E$. That is unless the market cap is priced according to the Direct Method, the two methods will disagree.

One can try to 'fix' the WACC method by Newton's method to recursively put $\tilde E$ values in the $R_{WACC}$ expression till one reaches a fixed point but this will just be $\hat E$.

So my question is why do people use the WACC method in the first place to find equity value when the incorrect equity value is an input in it in the first place.