Binary searches should be internalized as part of your life's vocabulary if you're a programmer.
You don't use all 10000 words of your native language every day. You don't ride a bike every day. Nevertheless, that's part of you and you don't need to make a conscious effort to remember which way the pedals spin when you ride a bike after a long hiatus.
I don't think those examples are really applicable here. You don't use all 10000 words, but our brains are evolved to process language and you interact with language everyday. Riding a bike has you engaging in a physical activity which is also something that we're geared to remember.
Programming is already pretty unnatural and implementing binary searches and other basic algorithms is really only something you do constantly in the beginning. Over time that "muscle memory" will fade. It's also something that's easy enough to look up and understand in a couple minutes.
You don't use all 10000 words of your native language every day. You don't ride a bike every day. Nevertheless, that's part of you and you don't need to make a conscious effort to remember which way the pedals spin when you ride a bike after a long hiatus.