That's the optics bit, I think. It isn't a safety issue for a driver waiting for the train they're taking over to sit scrolling TikTok on the platform (provided the sound is off - it's VERY bad optics for them to be sitting there breaching Byelaw 7 (1) (2)), but the optics are terrible - members of staff in uniform in any context, particularly safety critical contexts, with their head in their personal mobile phone just look bad for the company.
I totally get the point you are making about optics, but on the flip side several times in the past during disruption I've been waiting ready to relieve a long train towards one end of its booked long platform, where the announcements don't really reach very well. Had I not been following my train on Open Train Times maps on my own phone (drivers not given work phones there), then I might not have noticed it had been routed last minute on approach to the home signal into another platform, and not heard the announcements which sometimes don't give much advance notice anyway. Had I not been following it on my phone then this would/could have caused even more delay when I see it pull in on another platform and have to walk all the way back down towards the other end of the station to get over the footbridge/subway, then walk back along the length of the next platform to reach the front of the train. By which time the passengers are all on board waiting and the driver I'm relieving has been on the radio to the signaller and got the road put back due to thinking they've not got any relief.
This is obviously an example of something that mainly happens at just a few specific places where platforms and trains serving them are long but the bridges/subways are only at the other end, but an example of multiple times where had I not been allowed to use my phone within ten minutes of working a train and/or in a place the public can see me, then those trains and the customers travelling on them would have sustained even further - avoidable! - delay. The lack of company issued mobile phones means drivers tend to show goodwill using their own phones to make or receive calls to communicate with the traincrew supervisors, particularly during disruption, but if drivers had to have their personal phones off while waiting on platforms then this could actually hinder operations. I guess it would just result in the operator having to supply company issued phones to each driver and create a policy differentiating between use of personal and company phones, but then in terms of optics an onlooker will still just see a driver using a mobile phone and not know if it is doomscrolling Facebook or doing something that may actually aid their journey?
Finally, to clarify, I'm absolutely not suggesting drivers should be allowed to use them while actually in control of a train. Just that on multiple occasions the ability to use my personal phone in a visible location on a platform while waiting ready to relieve a train has actually helped reduce delays. Drivers are issued a somewhat more bulky tablet device, but does that really look much better from an optics point of view, someone staring at an even larger screen? Or is a tablet more likely to be assumed a work-related device from a customer point of view than a smaller phone? (Genuine question)