The only thing that's really wrong with this approach is that it's hard to make a very descriptive exception using assert statements. If you're looking for the simpler syntax, remember you can also do something like this:
class XLessThanZeroException(Exception):
pass
def CheckX(x):
if x < 0:
raise XLessThanZeroException()
def foo(x):
CheckX(x)
#do stuff here
Another problem is that using assert for normal condition-checking is that it makes it difficult to disable the debugging asserts using the -O flag.