First of all, using the ENABLE/DISABLE feature of the chip cannot be a solution here because even if the switching stops the output will be equal to the input voltage (neglecting body diode drop).
I was thinking of having a P-MOSFET on the output (after bulk caps) instead which is then ENABLED/DISABLE by a micro.
Well, this is a solution. The current flow on output side is lower than that on input side, so this allows you to select a smaller MOSFET. So yes, can be acceptable.
... anything else I should consider before putting the MOSFET on the output.
One other thing to consider here is the recovery behaviour of the converter output. Because the converter will keep running and the output will always be present (before the load), once the load is re-connected across the output the instant output current rise (i.e. step load change) will cause the output drop by some amount and then recover. This recovery, depending on the design (including compensation) and the load itself, may take too long or even may be oscillatory.
Similarly, once you disconnect the load, depending on the load state and design (again), the output will overshoot by some amount and recover. This overshoot amount may or may not be acceptable.
So you may want to check if the output voltage variation (drop amount or overshoot amount) and load behaviour under these states is acceptable.
Also the converter will keep running so the consumption will be high but depending on your application this may not be of a concern.
Any reason why the input side MOSFET seems to be the most recommended solution
Cutting either input or output is similar in terms of electrical design and simplicity (neglecting sizing the switch). Either a PMOS or a load switch IC will work but I personally recommend a load switch IC here as it's way simpler and some of them have built in over-current and thermal protection which might be quite useful.
Another advantage is that, unlike the dynamic behaviour that I tried to explain above, the load will take advantage of the soft-start feature of the IC so the output will rise from zero to its nominal gradually, and with almost no overshoot (hopefully). So, starting the converter loaded becomes less problematic.