There are LOTS of people like this and they and their tanks are fine.
This picture trotted out is probably from Europe. They often do not have burst disks. I'm looking at my Inspiration valve and there is no burst disk.
The comments regarding heat are not correct. A "hot" tank is not "10%" more full. At quick look at Guy-Lussac's law will tell you that pressure will double if temperature doubles. Take your 70F tanks and leave them in a 150F trunk and you'll probably lose your burst disk. If you leave a tank with no burst disk in a Nissan Pathfinder that caught fire you should expect the tank to explode. If you fill more modern LP tanks to 3500psi over and over you should expect that they will outlast you unless you let them rust to hell. Just use burst disks.
The pressure doubles if the temperature doubles. So if you go from 15 deg C to 30 deg C the pressure doubles? Sorry, you have to be measuring temperature in Deg Kelvin.