The sensors are needed because automatic garage doors without them (or with malfunctioning ones) can and do kill people, including children.
If your current opener has no photo-beam sensor, you should toss a 2x4 on the flat side on the floor and close the door - if it does not stop and reverse by itself when it hits the 2x4, then it also lacks (or is ignoring, or is massively misadjusted) the required pressure sensor reverse. The most likely cost-effective solution to that (other than adjusting) would be a whole new opener. The fact that your opener operates at all without photo-sensors is also an argument in favor of a new opener.
I had a main control board go bad after a nearby lightning strike which was causing the opener to try and drive the door through the floor - not a "fail safe" design on that one. You should check (and if needed, adjust) the safety systems at least twice a year, and any time the thing seems to be behaving oddly.
As for the kids smacking into the sensors, you can box the sensors into a more protected situation - and they do not HAVE to be mounted on the tracks - they can be mounted on the walls (the beam goes a little further, but the sensor is not hanging in space.)