By that logic there is no "work", only "heat". And that's simply not true. The useful work performed here is in moving heat from one place to another through convection. This is not complicated.
Next we'll be arguing that there's no useful work in the entire universe, only heat....
In the use of a fan, electrical energy is converted to work which is very
quickly and consistently turned to heat. Why do you think a fan makes a room hotter? Because it is converted electricity to heat. -anyway, this is fans.
In electronics there is zero work as the cycle happens so fast. Apart from the tiny portion of energy required to 'start' the cycle, all the conversion is from electricity to heat.
Again, in case I was not clear.
By your logic the Saturn V "did no work".
But there is a more profound error you make, which is in asserting that a fan, in moving heat from one place to another, "does no work". That's wrong, of course it does work. In fact, that's the very definition of work in a thermodynamic sense.
I replied to this conversation because it seemed interesting, but if you continue to stand on ignorance, this will get dull quickly.
What I was trying to point out is there is a difference between temporary and permanent work. Compare lifting a weight on a ratchet and our fan.
While lifting the weight, work is done and stored in PE. When you stop putting in work, it stays and there is a clear and stored outcome of the work.
With the fan, as soon as we stop the fan, everything has returned to pre-fan conditions. The air is a fluid so regardless of how you move it, it will still settle to a [now hotter] equilibrium and your work was converted entirely to heat.
In the case of your rocket, it clearly did permanent work as maybe 5% of the energy consumed is stored as PE above the earth. The rest was consumed as heat.