The problem essentially is that it's trivially easy.
There are plenty of non-dragonblooded Reman dynasty descendants to marry, and the rule about bastards not passing on the bloodline doesn't seem to work, at least for Graccus Rayles, so you don't even need to wait for a dragonborn to appear to relight the dragonfires. Imo there should at least be a 50% chance of failure to ignite the dragonfires if you have an imperial bloodline, but not dragonblood.
There are plenty of non-dragonblooded Reman dynasty descendants to marry, and the rule about bastards not passing on the bloodline doesn't seem to work, at least for Graccus Rayles, so you don't even need to wait for a dragonborn to appear to relight the dragonfires. Imo there should at least be a 50% chance of failure to ignite the dragonfires if you have an imperial bloodline, but not dragonblood.