Suppose that we model a price $P_t$ to evolve per
$$\frac{dP_t}{P_t}=\mu dt+\sigma dW_t$$
for $\mu\in\mathbb{R}$ and $\sigma>0$. The unique strong solution to this diffusion is
$$P_t=P_0e^{(\mu-\sigma^2/2)t+\sigma W_t}$$
My question is the following: by the law of iterated logarithm, one can show that as $t\to\infty$, the drift term $(\mu-\sigma^2/2)t$ dominates the stochatic part $\sigma W_t$, and $P_t$ goes to $\pm \infty$ depending on the sign of the drift. I am interested on intuition behind the following fact: if the volatility increases to $\sigma'>\sigma$, then $$(\mu-(\sigma')^2/2)<(\mu-\sigma^2/2),$$ So for $t$ big we have $$P_t(\sigma')\leq P_t(\sigma)$$ systematically. I understand this is due to Itô's correction, but I'm wondering at an intuitive level why, if the volatility is bigger, then the prices/value of a project tend to be smaller.
For reference of what I'm talking about, you can see this picture where I show two geometric Brownian motions, with the same draw of $W_t$, with the black one having a bigger volatility: