Of course small keys aren't safe. There are no checks for key nor for the seed words. Only important thing is that it was randomly generated.
If it was, then it would be pointless to check if it some small key due to the huge possible range of numbers it could be. If there was any realistic chance for a key to be small, then random number generator is not doing a good job in the first place and that would be the actual problem to solve.
If it is truly random, then your randomly generated private key could be
1 just as probably as anything else. I prefer to check that my randomly generated key is NOT very small or close to the biggest possible number.