or the reflector big enough to not be affected by the occlusion of the laser beam by the size of the LDR.... Simple.
Yes simple, it would simply not work.
Have you got any practical experience in this sort of thing? Your explanation sounds like a simple method that does not consider any of the practicalities.
The reason you need modulation for distance is that you need to amplify the signal from the sensor. This is normally a photo diode or photo transistor an LDR it totally useless in this situation.
If you amplify the signal from a sensor you are going to amplify the ambient light reading as well and quite soon the signal runs out of dynamic range and the amplifier saturates. So by using modulation you can simply AC couple into the amplifier and take out the DC offset bias.
Where, AWOL do you find 38Khz in a laser?
You can modulate a laser at what ever frequency you want.
a waste of time as we aren't trying to turn on the target or change it's channel
You can see from the above this is not true. It is a good idea to use TV remote parts because they are cheap and they do the job as good as anything else. Sure we are trying to detect the presence of a beam not send information to it, but it has to have the same characteristics as if we were trying to send it data.
What you seem to forget is that this is a gun trying to hit a target, not an IR blunderbuss trying to see if it is pointed roughly in the right direction.