Catching fish is theoretically not perfectly random (risk-averse fish are less likely to get selected/caught) but that's the best method in those circumstances and it's reasonable to argue that the effect is insignificant.
You make a very weak argument, and are simply assuming the conclusion.
What makes it the "best method"? Would it be better to use a seine, or a trap, or hook-and-line? How would we know if there are subpopulations that have different likelihood of capture by different methods?
To say it's "reasonable to argue that the effect is insignificant" is purely assertion. Why is it unreasonable to argue that a fish could learn from the first experience and be less likely to be captured a second time?
If what you mean is that it's better than a completely blind guess, then I'd agree. But it's not clearly the best method nor is it clearly unbiased.
Fair points. But, mark-recapture is about practicality. It's not perfect, but it's a solid compromise between accuracy and feasibility (so I mean best in these regards, to be 100% clear). Sure, different methods might skew results, but this technique is about getting a reliable estimate, not pinpoint accuracy. As for learning behavior in fish, that's considered in many studies (and many other things, like listed here: https://fishbio.com/fate-chance-encounters-mark-recapture-st... ), but overall, it doesn't hugely skew the population estimates. So, again, it's about what works best in the field, not in theory.