This is not the answer that you want to hear, but here it is, anyway: Do native speakers ever get 'bitch' and 'beach' wrong? No. Never. Can we distinguish between them without context? Yes. Of course we can! They are phonologically very different indeed. It is also essential for learners of English to learn to differentiate between these two phonemes. Learners who think that they're the same, or too similar to worry about, will spend the rest of their lives misunderstanding and being misunderstood.

To a native speaker of English these two words sound very different and, unless they have some knowledge of different languages' sound systems, would probably be surprised that learners from some linguistic backgrounds find it difficult. To us the vowel sounds are different, made with the tongue in a different position. It is not a question of vowel length. The reason you find it difficult is because, from a very early age, your brain became attuned to the sounds of your own language and concentrated on making the distinctions that are important in that language and stopped making distinctions that were not important. If I were to learn your language there would probably be sound differences that are obvious to you, but which I would struggle with

Mispronouncing the short i is what a native would stereotypically do to feign having a foreign accent.

I don't think so. It's the same of 'shit' vs 'sheet'.. You can hear easily the difference when someone pronounce that words without any context.