Why is RSA considered safe?
Yes, theoretically anyone can compute $\varphi(n)$ from $n$ and thus recover $d$ from $e$. This should be read as "given any $n$, it takes a finite amount of time to compute $\varphi(n)$".

More practically, "computing $\varphi(n)$ given $n$" and "factoring $n$" are equivalently hard. That is, if you can efficiently compute $\varphi(n)$ you can also efficiently factor $n$ and vice versa.

Now, if $n$ is sufficiently small, we can easily factor it and thus compute $\varphi(n)$ (which is what websites do), but as $n$ reaches cryptographically relevant values, it becomes infeasible (using current technology) to factor $n$ and thus to recover $\varphi(n)$.