I think you would have to offer more detail with your query, what type of work platform etc? What task? What environment?
I would not think a harness will add any benefit to fall protection and may even be a hindrance.
If the work platform is designed for purpose with correct edge protection, kick boards, hand rails and any designed intermediate rails then this should negate the need of a harness and fixed lanyard
If harness and lanyard is required then the anchor points should be designed so as to ensure suitability.
This should all be evaluated in your Risk assessment as per W@H Regs

In the example you give, and assuming the edge protection is suitable, then no harness is needed. You are preventing falls by the presence of the edge protection.

I'd question any safety policy where there is a blanket requirement to wear safety harnesses and lanyards at height.

As an aside, and depending on what legislation covers your site (UK or not?) the 1.8 meter rule no longer applies, the Work at Height Regulations cover any work where a fall could occur and lead to injury.

Edge protection is a "stronger" control measure within the hierarchy in any case and should always be considered before resorting to harnesses and lanyards etc.

The requirement of safety harness on 1.8 meter high platform will depend on level of risk involved to carry out the activity, any legal requirement, finally requirement of organisation's OH & S management system

1) I'm guessing you are talking about working on a MEWP (elevated platform) so YES, you would be expected to wear a safety harness in a Cherry Picker type (with a restraint lanyard) thus taking away the chance of falling out. The scissor lift type generally does not require a harness/lanyard of any type unless the manufacturer or RA calls for one.
2) There is no requirement to wear a harness on a 2m high scaffold platform, be it tube and clip or aluminium. The whole point of the main guard rail and mid guard rails are they are at a distance (470mm and 950mm) above the platform to negate the need for a harness.
3) As you stated before with the length of the fall arrest, you need to ensure you don't hit the ground before the lanyard fully extends. The W@H Regs takes you back further. The hierarchy is Avoid work @ height (by prefabricating for instance) then Prevent falls (guard rails form collective prevention) and finally, protection from the distance and consequences - safety harness with fall arrest, the last resort as Bob said.