As a supplement to the (excellent) accepted answer: phonemic transcriptions tend to be simple, convenient and easier than what is called "phonetic" transcriptions. It is way better to transcribe the English phoneme as /p/ than /pʰ/. Moreover, the underlying form is [p], that is, without aspiration. Aspiration is an extra feature in English. Because phonemic transcriptions tend to be easy and convenient, they are often called "broad transcriptions". They are not detailed transcriptions.

As a supplement to the (excellent) accepted answer: phonemic transcriptions tend to be simple, convenient and easier than what is called "phonetic" transcriptions. It is way better to transcribe the English phoneme as /p/ than /pʰ/. Moreover, the underlying form is [p], that is, without aspiration. Aspiration is an extra feature in English. Because phonemic transcriptions tend to be easy and convenient, they are often called "broad transcriptions". They are not detailed transcriptions.

And that is why phonemic transcriptions use /r/ instead of /ɹ/ because the latter is not available on ordinary keyboards and keypads (as Void says). The regular symbol (i.e. r) in the IPA represents a "trilled" r. The R sound in English is ɹ (or more precisely ɹ̠).