You could have called Nintendo and told them your 3ds was broken... I had an issue with my 3ds and I called them and they transferred my account to my new one with all the games... Granted it wasn't easy but I didn't lose anything...
I do agree their account system is stupid but there is a way around it for now...
PC Specs: CPU: 7800X3D || GPU: Strix 4090 || RAM: 32GB DDR5 6000 || Main SSD: WD 2TB SN850