As safe as possible yes, but only as safe as the phone is. Phone thefts will go through the roof I imagine, as they'll suddenly become much more valuable to criminals. Snatched out of your hand while you're using it (so it's unlocked) and, boom, they've got your ID right there.
My Polish digital ID card is secured via biometrics at every access. Snatching my phone won't achieve anything, as you won't be able to open the app, even if the phone is unlocked. You can use a password as well, but the password cannot be saved on the phone. So no, you won't have access to any details if you steal someone's phone.
There are plenty of employers verifying right to work, and landlords verifying right to rent who are being duped by physical ID requirements at the moment, which can be as little as a birth certificate and some other letter from some other government agency.
Right now, you can turn up with a handwritten Irish birth certificate and an easily faked letter from a UK government agency and voila, you've proven that you've got the right to work. I don't have a clue how an Irish birth certificate looks like, and neither do the vast majority of people in the UK.
If they don't then it still makes enforcement and prosecution much easier when the Border Force turns up. For everyone else who does play by the rules, it also reduces the risk of fake documents being used, as that chip shop owner would attest to.
I'd actually say that it makes everything so much easier. If Border Force turn up, then it's a very straightforward task to check these digital ID cards. No messing about with documents, no having to verify whether they're genuine or not, nada. If the system is done properly, it should be perfectly possible to actually record somewhere that an employer has checked a given digital ID card before employment started. Let's say some guy turns up and wants to start a new job. The employer can verify their digital ID card using their own digital ID card, and that verification can be stored in a write-once/read-many database. Border Force turn up, and they can instantly access that information. There is absolutely no doubt, and it reduces the 'right to work' checks to an absolute minimum while giving employers the certainty that the person in front of them is who they say they are.
Already answered in
#573. Why should you only be able to use it for one purpose when it can make your life easier?
It's ridiculous how much easier it is with a digital ID. On mine, I can see my car insurance details, I can see if my car is due an MOT, I can prove my entitlement to a discount on public transport, I have my driving licence, etc etc. All of this used to require endless documents, and now everything is stored in a single app. The brilliant thing is that it works for the public sector too: when I was last stopped for speeding, all they needed was my Polish personal identity number and they could check everything. No need to mess around with producing documents, no need to visit the police station, it was all there for them and they could see instantly who I claimed to be.
Or let's take another example: I needed to sort out something in my local council office recently. I went there and explained the issue, and instead of filling out yet another form, all I needed to do was use my digital ID card to authorise sending my information to their systems. They could then automatically fill in all the details, and then I digitally signed the form. All very nice, easy and convenient, and far more secure than relying on a handwritten form that might or might not have been submitted by me.
When I applied for a passport, I didn't need to take anything. They had everything available to them, all I needed was my digital ID card. They produced all the relevant documentation automatically, I signed my name on a tablet, confirmed my identity with my digital ID card and job done. No need to fill out forms, no need to bring documents, nothing.