I cannot fathom wanting an executive branch that’s more like the least functional democracy in the world. Yeah, maybe some bad things can happen from our system that couldn’t happen in the American. Maybe. But at least we have a government that can actually govern; that doesn’t shut down almost entirely because of the high probability that at least one of the three possible sources of blocking legislation (Senate, Reps, and Presidency) will be controlled by a different party from the other two.
At one time, America had a comparatively high degree of crossing the floor in their parties. Today, this is not the case, and because of that I do not have faith at all that a congress and presidency controlled by the same party would not have approved something like Robodebt via precisely the same means that it happened here.
The only way you could convince me to support an executive independent of the legislature is if you could somehow come up with a way to make it work like the courts: completely independent of party politics entirely, with roles appointed based on perceived expertise in a mostly-politically-neutral fashion. A directly elected president with political powers is a complete non-starter. (And that idea I had there is not even half-baked. I think I would be very unlikely to be convinced to support such a system based on the specifics.)