Humans can hear frequencies up to 20 kHz. Why don't hearing aids provide sound at frequencies above 10 kHz.

The previous answers bring up some interesting angles, but the real reason why digital hearing aids have an upper frequency limit is so that they can use a lower sampling rate when making the analog-to-digital conversion.

All of the signal processing features advertised in modern hearing aids to justify their price tag, such as noise filtering, happen in the digital realm.

Using a higher sampling rate would require more processing power in the chip, and in a unit as small as a hearing aid space is limited. Over the years the amount of processing power that can be packed into a tiny chip has increased, just as in computers and mobile phones. That's why many of today's hearing aids can extend their frequency response to 8 or 10 kHz, whereas eight years ago, 4 to 6 kHz was probably the standard.

Eventually, miniaturization will result in hearing aids that have a sampling rate of 44.1 kHz or even higher (meaning that the aids could produce frequencies up to about 20 kHz, do a Google search for "Nyquist 44.1" if you don't understand why). The issues raised about verification difficulties and the lack of norms for thresholds will not stop the hearing aid manufacturers from doing this. Why? Mostly, because music sounds much better when everything above 8 kHz is not discarded in the digital conversion process. Lots of people enjoy listening to music, and a small minority of people who wear hearing aids do not have significant hearing loss in those higher frequency bands, and would therefore much prefer listening to music through hearing aids that can reproduce them. The manufacturers want to please that small minority and increasing sampling rate is one of the logical ways to do it. If it also helps a very few people understand speech better in noise, then all the better.

As a case in point, Resound has already had sales reps visiting audiologists and asking them to listening to music through the latest Resound hearing aids which extend to 9.5 kHz.

Historical modern hearing aids amplify effectively to about 4000-5000 Hz and gain (amplification) starts rolling off significantly about 6000 Hz. That is starting to change, as one company now offers a device with meaningful amplification to 6000 Hz and even above - potentially out to 8000 Hz. There are phonemes (speech sounds) in the 6000 - 8000 Hz range and amplification at those frequencies could potentially improve clarity and understanding of speech. I have fit some patients with those devices and they really like the sound.

However, additional amplification in that high frequency region comes with a cost: We are much more likely to be battling feedback (whistling) when amplifying at those frequencies. When fitting the aforementioned devices, it has often been necessary to adopt a different fitting strategy (such as custom molds) in order to take advantage of those higher frequencies and still control feedback.

As technology improves, we will likely see more devices amplifying up to 8000 Hz. However, we tend to lose hearing above 8000 Hz very early. Many adults can not hear any sounds above 12,000 Hz unless they are almost loud enough to cause physical discomfort from the sound pressure. Most adults with significant high frequency (2000 Hz - 8000 Hz) hearing loss do not have usable hearing that is much above the 8000 Hz range. Therefore, I am not sure that we will ever try to chase frequencies above 8000 Hz, as no significant speech information is found above 8000 Hz and the majority of people with hearing loss could not receive significant benefit from amplification above 8000 Hz. It would truly not be worth the effort.

As frequency rises, the likelihood of cochlear dead zones increases. This means that amplification of very high frequencies is likely to produce excess distortion and be counter-productive for speech understanding. Secondly, high frequency speech sounds are produced with very little energy and where hearing loss is greatest. Therefore high levels of gain would be needed to achieve audibility. This is impractical because of inevitable feedback. 

The simplest answer is that the information we need to understand speech does not exceed 10,000 Hertz.  Technology is designed to provide the brain with sounds that will assist with communication. 

 Humans can hear above 6000 Hz but we lose the ability to discriminate one frequency from another frequency above about 10,000 Hz. Therefore information above 10,000 Hz isn’t very useful to our brains, in the same way that it could be useful to the brain of another animal, such as a dog for example.  The primary focus of auditory rehabilitation using hearing aids as to amplify the information contained in human speech which ranges from about 125 Hz to 6000 Hz. 

Speech doesn't go up to 10k. We fit for speech, not noise, and personally, I don't care if you can hear a bird in the backyard. If you can good, but speech is what we care about.