I guess that those aren't seen often because they require the phonology and grammar to be already close to finished - or at least enough to know which constructions are used so often that get contracted.

That said I full agree with you, they're awesome when done right. They're when the conlang stops being a bunch of sketches in a book to become something living, at least in the mouths (or gestures) of imaginary speakers.

Since the phonology of my main conlang (Tarune) is finished, but the grammar is still heavily WIP, my only progress in this regard was creating a formal register vs. local pronunciations. Not quite what you're asking about, but close enough, so I'll share two examples here:

Hiatuses between words

In the formal register you're supposed to dissolve them with [h]. However, people in Central/Northern cities don't do this bother in quick speech. Example:

• Romanised: ⟨Sobeca ep Lorā⟩
• Phonemic: /su.bi.ca ip lu.ɾa:/
• Phonetic (formal): [sʊ˥.bɪ.cɐ hɪp lʊ˥.ɾä:]
• Phonetic (Central/Northern urban, quick speech): [so˥.be.cɐɪ̯p lo˥.ɾä:]
• Translation: "Sun and Moon"

And it's hard to represent in IPA, but Central speakers have a tendency to shorten the long vowels. They're still distinct from the short vowels, but in quick speech you're telling who's who by the quality, not by the quantity.

Rendering of voiced consonants

In the formal register, when a voiced consonant or consonant cluster is near a nasal vowel, you're "supposed" to nasalise it midway: a single consonant gets pre-/post-nasalised, and in a cluster only one consonant gets nasalised. In practice... well, only people in the coast do this in a natural way. The others either don't nasalise the consonant at all, or do it fully, like this:

• Romanised: ⟨Duamde⟩, ⟨ṭelsemd⟩
• Phonemic: /dwã.di/, /ʈil.sĩd/
• Phonetic (formal): [dw̃ɐ̃˥.n͜dɪ], [ʈɪl˥.z̃ɪ̃n͜d]
• Phonetic (C/N, informal but increasingly common): [dwɐ̃˥.ne], [ʈel˥.zẽn]
• Phonetic (Southern, #1): [nw̃ã˥.ni], [ʈil̃˥.z̃ĩn]
• Phonetic (Southern, #2): [nw̃ã˥.di], [ʈil̃˥.z̃ĩd]
• Translation: "Southern Wind", "45 days month/season"

So it's a lot like the Central/Northern speakers shifted the nasalisation to the right, while Southern speakers either spread it further or shift it left.

EDIT: ah, Southern backchannel ['u:˥˩ʔu]; typically spelled ⟨ōho⟩. This... interjection? has a weird story - it was initially used by cattle herders to direct their cattle. Eventually the usage spread towards humans too, to convey "are you following?"; and then as backchannel, to convey "I'm following it, go on".