It would be good to understand the reasoning for some of those items, particularly if travel isn't long distance or remote. But personally, I think some of those items should be in a vehicle by default - torch, hi-vis vest, 1st aid kit, gloves.

Evaluating the nature of the travel, the travel routes, time of day, likelihood of other vehicles coming across you if you were broken down, etc, could be a good place to start.

Suggest checking WorkSafe https://www.worksafe.govt.nz/managing-health-and-safety/businesses/general-requirements-for-workplaces/first-aid/ for requirements as well.
First Aid at Work Feb 2020 resource has:
'You must provide a portable first aid kit in the vehicles of mobile workers if that is their workplace (for example, couriers, taxi drivers, sales representatives, bus drivers, inspectors). The kit must be located in a secure place within the vehicle, where it will not move and cause injury or damage in a collision."

Hi Sandra. We had something recently come up about first aid kits in vehicles and the opinion leaned towards doing a risk assessment and being pragmatic. I think the same would apply here.

Are emergency hammers and car escape tools the same thing? What do you need to escape from? Is the vehicle at risk of becoming submerged? Low speed travel around your average town without any nearby bodies of deep water might suggest otherwise.

Likewise, a tyre pressure gauge isn't so much an emergency item as a general maintenance issue. Electrical tape might be the same. Handy, but necessary for emergencies?

Personal alarms are a personal safety issue and quite separate from a car emergency imho - how can a personal alarm in the emergency kit help if the emergency kit is stowed in the boot? Where are your staff travelling and what situations are they being put into if personal safety is an issue that merits a personal alarm? I'd suggest you have a bigger issue if staff are asking for personal alarms.

As Alex P says, some items are very useful and should likely be included - hi-vis vests, a small first aid kit, perhaps a torch (bear in mind most people have mobile phones with lights these days).

I'd start by doing a risk assessment and thinking about the job and the hazards to which the worker is likely to be exposed to.

It might also be useful to go back to the employee and talk to them. It would certainly be good to understand why they think their personal safety is at risk rather than simply declining to provide a personal alarm.