So a transcription with diacritics is always going to be a narrow transcription?
No! It depends on the language.
A diacritic records a detail about a pronunciation. Whether or not you get to ignore that detail in a broad transcription depends on whether it can change the meaning of a word in the language you're transcribing. If that detail can change the meaning, then you need the diacritic even in a broad transcription.
It's true that you can do broad IPA transcriptions of most western European languages without using diacritics (which shouldn't be surprising, since the IPA was originally created by western Europeans who wanted to do broad transcriptions of their languages without using lots of diacritics). But it's not true of all the world's languages.
In fact, for almost every diacritic symbol listed in the IPA, there's some language somewhere that needs to use that diacritic even in a broad transcription.
Well, if Canadian French has no difference in meaning between [liv] and [lɪv], then why write it [liv] in a broad transcription? Why not write it [lɪv]?
That would be perfectly legitimate too. But one of the unspoken principles of the broad transcription is that, when you're given a choice between two symbols and when all other considerations are equal (sometimes even when they aren't), you'll pick the one that's easier to type.
But doesn't writing both [i] and [ɪ] as [i] violate the "one sound, one symbol" policy of the IPA?
Yes and no. It depends what you mean by "one sound".
At one level, [i] and [ɪ] are clearly two different sounds. Trained listeners can hear the difference. The mouth does slightly different things to make them. You can see the difference in fancy computer analyses. It's this fairly physical sense of "one sound" that a narrow transcription is interested in.
At another level, [i] and [ɪ] count as the "same" sound in the minds of speakers of Canadian French. Without training, most speakers of the language may not even be aware of the difference. You can switch one sound for the other and you won't change the meaning of any words in Canadian French -- at worst you'll sound like you have an accent. It is this sense of "one sound" that a broad transcription is interested in, so a broad transcription will use one symbol to cover both sounds.
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