ID Card (or PP) is mandatory for 15 years and older. Getting an ID card much younger should not be an issue (getting a PP neither). One of my kids did have an ID card with 13 or 14, which she showed to me. She did get the card earlier on, before she did come to PP. She just turned 17 and is for more than 3.5 years in PP now.
And with National ID, border traffic is possible (family did), though it could be "not officially", or limited to only the border town for a limited time, though who checks that area limitation. And what could immigration do, when somebody shows up for return, without a Visa stamp or whatever showing the outgoing date.
For example, the Koh Kong border is very chaotic, that there is limited control who passes the border in either direction. Heck, I planted my luggage in the ongoing cab, some 50 m from the border, before obtaining my visa (for the regular instead of elevated pricing). The immigration officers aren't posted at the barrier, but just sitting in their building, without real sight on the barrier itself. There is also a market at the Thai side, where Khmers "just go" for their veggies and whatever Thailand has on offer.