With regards to multirate processing, what are the benefits of having a 'slower' sampled signal?
In addition to what hotpaw2 said, it's important to understand that sample rate reduction is the corner stone of actual applicability in many systems.

Software Defined Radio frontends nowadays produce hundreds of complex-valued Megasamples per second – if you don't reduce that amount of data, no commonly available PC can deal with that.

Also, many devices that you meet nowadays actually have software-programmable DSP embedded very deeply. The average mobile phone baseband IC, i.e. what handles the signal, is digital and very broadband, to "get" the whole bandwidth that e.g. LTE demands they can capture; however, at a single time, only a fraction of that bandwidth might be relevant. So isolating/extracting that bandwidth is crucial to functionality.

Not reducing the sample rate in that situation would not only be a pure waste of power – it would render the following steps, such as equalization and synchronization, totally impractical in the telephone form factor.

A movie camera might take up to let's say 16 Million pixels – which are, in the end, nothing but samples of a twodimensional signal! If the producing camera didn't remove that sample rate (i.e. the picture's resolution), there's no way that the resulting movie data would fit through the terrestrial TV channel; no way that a cheap TV might decode it, and no way you could by such a movie on a cheap optical disc at current capacities.

So, this, by far, is not a "historical" problem. It is a very current problem – not being able to handle the full sampling rate that ADC/DAC hardware offers is the core technological problem of pushing communication further. 

Now, 10 kHz really isn't something you'd normally worry about – that's something that most algorithms could deal with on the cheapest microcontroller. But think more in the terms of a SDR frontend (e.g. this one) that has 200 MHz of sampling rate per single complex ADC; that means that you can't even get the  two channels of that device into whatever computer you attach at the native sampling rate, because $2\cdot200 \cdot 10^6 \frac {\text S}{\text s} \cdot \frac{16 \text{ b [I]} +16 \text{ b [I]} }{\text S} = 12.8 \frac{\text{Gb}}{\text s} &gt; 10 \frac{\text{Gb}}{\text s}  $, which is the datacenter-grade 10GbitEthernet interface's data rate that usually totally flattens out even the most powerful quad-core PC CPUs, without them even doing any DSP, just shuffling the data into RAM. Now, you realize that for almost all applications, it's very desirable that the device internally reduces the sampling rate of the observed signal as far as possible to correctly represent that signal, for computers to even be able to cope with the raw amount of data. The device does that, by applying cascaded multirate filters internally. The ability to, nevertheless, observe the whole bandwidth at once and "select" any part of these 200 MHz at random is very crucial to designing things like wideband transceivers or frequency-hopping standards; so the ability to use the minimum viable sampling rate is very central to progress in research, application development and implementation, as soon as you're not considering 10 kHz systems any more.