Trapping can be effective with very simple equipment and a properly designed and constructed trap should either kill the animal outright (preferable) or not be easy to escape from.
Also bear in mind that in many cases improvised traps may be illegal (in a non-emergency situation) so it may not be possible to test them in real world conditions.
Trapping is not just about being able to build the trap itself, you also need local knowledge of animal behaviour and geography to have a decent chance of a trap being effective for example knowing what species are in a particular area, which are worth targeting and where to place a trap for it to be effective.
The big advantage of trapping it that it can provide you with high energy food for relatively little physical effort. Equally in a longer term situation just the fact of doing something positive to improve your situation can be an important psychological factor and any success at all will be a big moral boost.
Whether or not it is worth your time to learn is really up to you to decide. It is fairly unlikely that you will end up in a situation where lack of food becomes a life or death issue and you also have the opportunity to set up traps.
Certainly I would say that it is a fairly low priority as a survival skill compared to things like making fire, finding water, navigation and medicine.