OK, let me focus on unicorns. I'll list only some possibilities and a creative person can surely invent more justifications. Note that you can apply different justifications for different types of creatures and if you think it's good for a game balance some of the reasons might be for example overcome by let's say getting more skills increasing the loot changes as your character develops.
Be creative and you can find other reasons as well for sure.
Note, some of those examples were already listed in previous answers, but I was always trying to add something from myself. Some are entirely genuine.
Not all horns are suitable
Think of a pearl. Not all shelled mollusk contain one and those that contain it usually have imperfect ones. Chances of finding a perfect one is likely less than 1:100. Similarly the unicorn horn might grow in various ways and only if it's given perfect conditions (e.g. no horn usage until the unicorn matures) the horn is properly shaped and can hold the magic. Depending on what you want to achieve from gaem balancing perspective you might have a possibility to distinguish "good" horns from "bad" before killing the creature or not (again - a skill that might be developed over time). Also you may have some sort of horn quality graduation (starting from those 96% totally useless, 3% average useful and 1% super high quality horns that are required for the most complex magic).
Another option is a rare mutation that causes the horn to have a different build. Again depending on the needs you either can't tell without killing the creature (the core is different) or you can (with increasing skills - the coverage is slightly different causing the horn to have slightly different shade of white, you need skilled eye and probably some magic to distinguish that from a distance or even closely - note you might not now if your horn is useful or not until you actually use it or find some other way to distinguish)
Horns get damaged during the battle
They can get damaged in a battle or it can get damaged over the time. Each option gives you additional opportunities.
If the horn can be damaged during the particular battle you might increase your chances by being more skilled and fighting in a less risky way (stealth kill?) - a skill that can be developed over time.
If the horn is damaged over the time you might learn to notice the difference before killing the unicorn. Again a skill to develop to be able to distinguish if the curse for killing the unicorn is worth it. In such case you might increase your chances by choosing younger unicorns. On the other hand the more mature creature is the more powerful the horn might be.
The horn gets damaged while looting
Horns are built of keratin that can be easily damaged while you're trying to detach the corn from the corpse. Of course you can always give it a try but you're lucky only 1 time in 100.
Again you can increase skills and that way increase your successful looting chances.
Stress causes horn damage
Of course it can be limited to magical abilities. You can't kill the beast not causing its stress however unicorns some might be more stress resistant and as a result the effect does not remove magical capabilities of a horn entirely. You can't tell from the distance and you can't tell to what stress was the unicorn already exposed.
Again a real life example. If you consider carp, this fish has a bad PR for it's intense "fish-like" taste. The truth is the flesh of carps get the taste when the fish are exposed to stress. The less stressful way of killing the fish, the less effect on the flesh taste.
Horns quickly loose their magical capabilities unless properly prepared
This time you need to act quick. But even creatures position might impact how quickly can you detach its horn. In this scenario killing from a distance actually reduces your chances of a successful loot. Skills can also be developed as well as you might need to have some other ingredients or mana power for a proper horn preservation.