A couple quotes from some of my trip reports that touch on this subject:
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I crawled up, and bow-n-arrowed into the tailout, hooking and unceremoniously skipping a dancing little brown down and out, releasing it into the cut below. Now for the cast that matters. In fast mountain streams, and depending on insect activity and specific pool layout of course, tailouts more rarely hold good fish than they do in slower more fertile streams. Here, fishing the tailout is more a matter of removing the 6 or 7 inch potential pool spookers that are kept off the better lies further up the pool by larger fish. The next cast went to the back end of the basin and was met with a smacking rise. I paused, lifted, and a nice brown responded with a remarkably high tailspring, then another, and another, spitting the dry fly. But, I had previously attached a dropper nymph to the dry’s hook bend and, as not uncommonly happens, the dropper line slipped through the clenched mouth of the escaping trout and re-hooked it on the nymph. Another tailspring –which took the fish out through the tailout and into a tangle of willow roots below. My line hung lifeless in the air. I snatched it and said, “Rats!”, and then, “Wow!”
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Normally I'd try to catch these tailout fish and pull em down and out so as not to alarm the rest of the pool. But this is less an issue on such turbulent high gradient streams than it often is in flatter gradient water, where a single spooked 6inch trout can freak out the entire pool. In these steeper waters, a small trout zipping up doesn’t ruin the pool, in fact it can even help me out. Some of my better fish for the day came when I missed or pricked a fish which caused it to bolt. A shift then occurred in drift site occupancy, and several times during the day a larger trout dropped down to occupy a station near the tailout, and into casting range. …
I've spent a fair amount of time watching anglers approach pools and watched the trout's reaction. Most anglers, unbeknownst to them, spook the majority of feeding fish before they even set to cast, or with their casts.
And as Sasso mentions, patience can make all the difference.