I'll try to answer it: I think you just want to move units around so h (Planck's constant) has units of Joules instead of Joule-seconds. While this works mathematically, it doesn't really make sense physically, where we care about the energy of a photon because that's the value that is conserved (along with momentum, also relating to h) during any interaction (e.g. the quantity gained by an electron if the photon is absorbed). It really doesn't make sense to want to quantify the "power" of a photon, which doesn't have any physical meaning, in favor of a simpler constant.

You are right about the constant 'h' having a "hard-coded" 1-second built in, but so do ALL derived physical constants . If we, say, changed it to two seconds, the number would be cut in half to reflect the scale change and preserve the energy of the photon (or any action) because that does not depend on scale.

As to "why is it Joule-seconds?": that's the discovered law of nature. If the energy was proportional to frequency squared, h would be in units of J*s².