Hi Sarah
There are two issues here:
1. Should they have a helmet?
2. If yes to that, should it have a chin strap?
The risk assessment should enable the appropriate answer to both questions (and more).
The first part of that assessment is about what type of MEWP.
In broad terms you have scissor lifts which only move up and down (though most can also travel, but generally shouldn't do so when the platform is elevated).
....and then there are the MEWPs with booms which can go in multiple directions.
So, if you have a scissor lift and there is nothing above, may be there is NO risk of e.g. striking roof members, so perhaps the only thing likely to land on the head is a falling meteorite, the risk of which is usually going to be so negligible as to mean that the helmet is probably OTT - though MIGHT well be a site wide blanket rule.
Much more scope for the head to be struck or to strike something else when in a "cherry picker" BUT a typical industrial helmet is only designed to protect against falling objects, not LATERAL impacts.
....a large scale study in the US in the 1980s concluded that over 60% of head injuries in construction were to parts of the head OTHER than the crown, so the typical industrial helmet provides little, if any, protection against those 60%.
[HSE's lab people, HSL published a report that quotes the US study at about the time the long since revoked Construction (Head Protection) Regulations 1989 came into force]
So, may be what they should be using is higher spec helmets with absorptive materials between the harness and helmet shell. [A typical helmet relies on an air gap between the crown of the shell and the harness to absorb the residual force of an object dropping to the helmet and penetrating the shell - so for added protection you replace that air gap with absorptive material not only to the top but also to each side- so similar to helmets used by e.g. firefighters, motorcyclists and mountain climbers].
Second question - in most scenarios a chin strap will NOT provide the user with any significant protection. It is often put forward as providing protection should somebody fall from e.g. a cherry picker but it won't make a lot of difference if somebody falls say 6m and smashes their head with or without helmet against the ground or some hard object on the way.
What the chin strap DOES do is provide protection to others who might be at risk if the helmet comes off.
So as example it is mandated on works on high speed roads - helmet flying off presents a risk to passing traffic.