Draw bridges seem to be a staple of the castle era. when my kids build sand castles they automatically add moats and draw bridges. But were they common? Building bridges seems hard enough. Building bridges on hinges as a security measure during the castle era seems like a huge undertaking. Did this happen a few times and entered into lore, or were draw bridges an actual pervasive thing?
Probably not the best answer but...
Moats (and therefore draw bridges) are seen more often in English castles where the ground was more level. This would add artificial height to the walls of the castle, and make it harder to assail. Castles throughout mainland Europe had better terrain advantages, such as being built on the side of a mountain, so moats and draw bridges are not seen frequently in those areas.
Draw bridges were also not always "draw-able." A simple wooden path to the portcullis could easily be set alight in the even of an attack, and serve just as well. There are also accounts of just large beams being laid across the gap and can be drawn back as needed. Much cheaper and easily replaceable. Larger (i.e. more expensive) castles in the later Middle Ages did have retractable, true drawbridges, but considering all of the reasons to now have them, the cost, and engineering of the time, they were not as common as we think, and more romanticized.