Why should an electric heater not be daisy-chained?
The first recommendation would be related to the amount of current such a device draws. If one uses an outlet multiplier or a power strip, one can add other devices which would increase the power draw, placing the chain in danger of overheating, fire or tripping a circuit breaker. One could argue that the operator can take the responsibility of not connecting other devices into the multiplier. This can be valid, but legal statements such as these "protect" the manufacturer.

My experience with outlet multipliers is that the quality can be suspect. A poorly made one may work fine with today's lower power electronics but have failures when subjected to high currents such as those drawn by heaters.

The second caution follows that heat generated by the heater should be be applied to the power outlet and power cord.

I have a different stand-alone heater which is connected to a power strip. The power strip power cord does not get warm, but the heater cord does get warm. If both levels of heating are engaged on the heater, providing maximum heat, the power strip pops/opens the breaker circuit, terminating power.

This places the responsibility of safe operation on me and I never activate both levels of heat simultaneously.

One could expect that if you observe caution, you can be successful operating your heater in a manner inconsistent with the safety instructions. If you can trust that others in the household will also use appropriate caution, all the better.