LTspice not getting exactly -3dB point
First, your transfer function is not correct. You can see this must be true because your \$H(s)\$ has a pole at 0, while the actual response has the pole at ~300 Hz. I calculate

$$H(s) = \frac{1 + s(R_2C_1)}{1+s(R_1+R_2)C_1}$$

You could also write this as

$$H(s) = \frac{1+s/z}{1 + s/p}$$

where \$z = 1/R_2C_1\$ and \$p=1/\left[(R_1+R_2)C_1\right]\$. 

Next, when you assume that the response is exactly -3 dB at the zero frequency, you assume that the pole is having no effect at that frequency. That is, you assume

$$1 + s(R_2C_1)\approx 1$$

But this isn't exactly true, so you don't get exactly -3 dB at the pole frequency.