Practically, this just introduces the $\frac {(\Delta t)^2} 2 \ddot x^t$ term to the position update

It seems like we have effectively added the quadratic term from the Taylor expansion of x(t + dt). I wonder if we can keep adding more terms to Get a more accurate estimate?

Here, we have a derivative in the future. To my understanding, this term, velocity at t + delta t, made it so implicit Euler is quite complex and requires a lot of implementation and computational difficulty. Why does this term not make Modified Euler hard? If anything, it seems a bit more difficult than implicit because this has the future derivative and the current derivative.