If the design of a hard hat reduces visibility significantly, it's the wrong design to be using *outside* the cab where you're more likely to need to look around to ensure something isn't about to whack you in the face. Let alone inside it.
Outside the cab you can turn your upper body as well as your neck and you haven't got a restricted space around your head either. In the cab you have a fixed seat and a set of controls in front of you so being able to turn your head easily without any unnecessary restraint would be a priority for me.
The PPE at Work Regs 1992 say
Assessment of personal protective equipment
6.—(1) Before choosing any personal protective equipment which by virtue of regulation 4 he is required to ensure is provided, an employer or self-employed person shall ensure that an assessment is made to determine whether the personal protective equipment he intends will be provided is suitable.
(2) The assessment required by paragraph (1) shall include—
(a)an assessment of any risk or risks to health or safety which have not been avoided by other means;
(b)the definition of the characteristics which personal protective equipment must have in order to be effective against the risks referred to in sub-paragraph (a) of this paragraph, taking into account any risks which the equipment itself may create;
Given that the driver is in a cab -which is your protection "by other means" - what extra protection is a hard hat going to offer? In my view (admittedly only 30 years qualified in this area) to insist on extra clobber is self-defeating and more likely to increase risks. Unfortunately lots of poorly-qualified writers of risk assessments and the safe systems of work that should
follow the RAs can't see it either.
Now if your man is walking round the site with a hand-held radio controller, I would agree with you, as you are reducing the risk by letting him get closer to the actual lift. In this case it would probably be better to have a special hard hat with no peak though.