Phones are a "thing" because they were the first decent method of objectively and accurately recording unwritten languages (in the 19th century). Back then, if you heard a Lushootseed speaker translate English "The bear ate the salmon", the standard practice was to guess with untrained English-speaker ears that the person said "Oo uhshluh tube tea skuchicuss uh tea spots". Because tape recorders and even wax cylinder recorders did not exist, there was no decent way to say how the utterance was actually pronounced. "Phones" are simply standardized transcriptional symbols that have a (relatively) fixed meaning in terms of what appropriately-trained people hear (i.e 'ʃʲ' should sound a particular way, no matter what the language is). When you start getting into whether a particular sound is "important" in a language, that is where you get into phonology and "phonemes".
The concept of "phone" became systematic in linguistic practice in the 30's onwards, during a period of methodological frenzy. The idea was that you have to first start by writing down what was actually said (given knowledge of the symbols and competence in distinguishing "ʉ" from "y"), and this is recording in terms of "phones". This is basically the conversion of a continuous physical signal into a discrete symbolic representation. After you've got this reduction of speech to phones, you can analyze the distribution; you will record for English such phones as [t, tʰ, ɾ, t˺, t˟], and yet you notice that these sounds never appear in the same context (as happens with "tie" versus "die"). Thus phones are grouped together into sets: a set of phones that never is the basis for distinguishing utterances (very roughly) is a "phoneme". Choices of phoneme is what makes different words different (in sound). Hence the view that phonemes are about perception.
The main problem with saying that we perceive in terms of phonemes is that this is simply false, or requires a special definition of "perceive". There is a classroom stunt that is often pulled on students in phonetics-phonology classes, where you record a speaker saying "stick", "tick" and "Dick", then edit out the fricative from "stick", and playing the words, ask the students to identify the words. Edited "stick" comes out as "dick". The "explanation" is that English has the phonemes /t,d/ and the phones [t,tʰ,d], and speakers can't "perceive" the phone [t] as distinct from [d], they only perceive the two phonemes.
The flaw in this is that it's task-determined. Speakers can correctly identify edited "stick" as being distinct from "dick", and they can tell if a person uses the "wrong phone" in pronunciation (e.g. saying [stʰɪk]). It's not that we can't perceive low-level predictable details, it's that we disregard them for most especially linguistic purposes. Also, people are able to learn new languages with new sounds, but that would be impossible if you could only perceive the phonemes of your language. You can actual learn that German "bieten" and English "beaten" are pronounced differently albeit quite similarly.
There are, however, quite a number of physical differences which quite literally cannot be detected by people, for example the difference between a tone at 200 Hz and one at 201 Hz. The concept of "phone" may have utility in distinguishing sound-differences which are completely incapable of being linguistically exploited, versus ones that happen to not be exploited in a particular language (like aspiration in English).
If the goal is to do speech recognition on English (or some other well-understood language), then "phones" are completely superfluous. We already know what the range of acoustic variation is going to be for "p", "f" and so on, and we can adjust our programs (database) accordingly. Phones are more important in that first stage of mapping speech to symbols. They continue to be important for quite a while, because we still don't know what a "phoneme" is. For example, we do not know if [ɾ] is a phoneme of English (everybody seems to have their own opinion, there is no scientific consensus).
Here's the bottom line for perception and phones. There is a limit to what kinds of sound differences can be distinguished by humans; there are also limitations where one's prior linguistic knowledge influences you (to perhaps not notice the difference between "bieten" and "beaten"); then there are differences that you really just can't miss, assuming you already know the language. "Phones" are about the middle class of problems, where you can hear that sounds are "somehow different" in a systematic way.
(The Lushootseed example is [ʔuʔəɬətub ti sq'əčqs ʔə ti spaʔc]).