The No Free lunch theorem is basically a consequence of the fact that almost all problems 'look random'; it doesn't really apply to the tiny subset that are of interest to humans.
You can read more in: Antipredictable Sequences: Harder to Predict Than Random Sequences by Huaiyu Zhu and Wolfgang Kinzel
That's a very misleading TL;DR. NFLT certainly _applies_ -- deep networks are not immune to NFLT -- it's just that NFLT isn't very useful because we can't use it as a basis for decisions. You can't detect that your algorithm's performance is being limited as a consequence of NFLT; and even if it were consequential, you would just see that the algorithm wasn't working very well, and there are _much_ more likely causes for that than NFLT.
In other words, for any pair of machine learning algorithms there is an algorithm which only performs marginally worse than either of the two on any given problem, and which may perform arbitrarily better. NFL equalises these two cases by smearing tiny losses over vast regions of possibility-space that are vanishingly unlikely.
Is there a resource I can refer to, that is clear and explicit about the reasoning?
If we didn't care about resource usage then we could just pick a sufficiently expressive model class (e.g. all algorithms) to mix over, and perform Bayesian inference. You can look up AIXI and Solomonoff induction for more thoughts along these lines.
The subtle elements of the theorems (both for inference and search) have had huge impact on the field of optimization theory. They touch upon (Kolmogorov) Complexity, Incompleteness, Halting Problems, and later related work on the physical limits of inference: One can not know everything about the universe, if you are a part of it, and philosophy: Is the universe itself a computer?
That different algorithms and search strategies will succeed for different tasks, does not imply that we have to try them all: We can use prior knowledge on what worked on related tasks. Also the tasks we care about, is only a very small (explorable) subset of all possible tasks.