Click chemistry has been a major force behind the development of innovative technologies in materials science and chemical biology. The general accessibility and ease of protocols has been a welcome bonus point, especially for those who are not trained in chemistry. If one can figure out how to place an alkyne and azide components where they need to be, this kit-like approach to building molecules from simple blocks can be tremendously enabling: all you need is to add a copper catalyst. There are also copper-free protocols for running triazole synthesis. These surrogates often hinge on the idea of strain relief (Caroline Bertozzi has been one of the pioneers in this area).
When I attended the 2016 Gordon Conference on Peptide Chemistry and Biology a couple of weeks ago (this meeting was superbly organized by Phil Dawson), I got to hear a thought-provoking talk by Jim Heath of Caltech. He uses click chemistry in order to discover macrocyclic ligands for epitope targeting. Because the presence of copper adversely affects biology, Heath uses the copper-free protocol. However (get this), he is not using any strained alkynes… When I heard it, I got really curious about the underlying reasons for how might a pair of molecules react in a [3+2] fashion at room temperature without any “extra help”. I asked Jim this question and found out that there are, in fact, no miracles here: his yield is abysmally low. While I appreciate that this is not a preparative reaction, I really wonder: why would one want to use the azide/alkyne cycloaddition here to begin with? I would hazard to guess that this constitutes the least interesting of all processes that could be run in the Heath format. Personally, I would be much more interested in looking at some of the pillars of chemistry (amide bond formation?) under his conditions. Sometimes truly interesting things might arise from more conventional processes, and it might also be easier to put together the starting materials. But this is just my view.
http://onlinelibrary.wiley.com/doi/10.1002/anie.201505243/full
amphoteros 
FYI, there are few non-strained elctron-deficient alkynes that react with azides at a reasonable rate even without copper: CF3CΞCCF3 and EtOCOΞCCO2Et.
Also, I have been making the BCN strained cyclooctyne linker alcohol (sold by Synaffix) in gram quantities and it is pretty easy, based on the Angew Chem procedure that can be completed within 3 weeks. It is something that an undergrad can do.
By all means, this makes sense. However, if there are no activating groups, the barrier is way too high. I was just amused by the fact that people would still use this reaction in cases where it appears to be a total overkill (in my view). Thanks for the BCN comment.