I don't think looking for second monitoring capability is a sign of distrust. I think it's just a Dad being a Dad, and wanting to NOT interfere with his daughter's experience.
When I used it, I trusted my buddy, but knew that task saturation can lead to channeled thinking. Wouldn't it be nice for me to see gas being used rapidly and unnoticed by the primary diver, and at the right time "ask" for a pressure check? The unexpected arrival at reserve gas pressure serves as its own lesson for the young diver who might have not been keeping track.
And if the daughter is on top of her supply, then Dad gets to watch unobtrusively, be proud, and just relax. The whole question seems perfectly appropriate to me.
You are an instructor, I'm not, so I'll defer to your experience with new divers. But seriously, think about this. Such a device is really playing into the soft bigotry of low expectations.
I'm a dad. I know how terrifying it is to dive with your kids, and wonder if they will be able to handle the awesome responsibility of keeping themselves alive. But if you can't accept that they are capable of doing that, they shouldn't be diving with the crutch of you watching their air supply.
Do you feel that all new divers should have their tank pressure continuously monitored by an instructor? If not, why not? Aren't their lives just as precious? If a diver's monitoring of their own gas supply results in too much task saturation, then that diver shouldn't have been given an OW card. That and "keep breathing" is literally the most basic thing that any new diver has to do.
Even if we are talking about some sort of "trust me" discover diving thing, ask them for their gas supply by hand signals. Do it often if necessary, so that they get a sense of how quickly the gas is going, and of how communication and situational awareness is suppose to work. Once every 5-10 minutes or so is fine in the beginning, there is no need for "continuous" monitoring.
But if we are talking about a certified diver, there is no excuse for not being totally, 100% on top of their remaining gas reserves. If your teenage kid gives you attitude about asking them their tank pressure, then tell them that they can pay for their own diving once they are 18.
Setting the bar so low doesn't make you a better diver, a better mentor, or a better dad.