Definitely. I'm not saying the word 申請 itself isn't used in normal speech, but more that the pronunciation of 請 in normal speech would sound more like an e. So I would rather teach people the normal way people would pronounce words and not the literary form, since as I said before, I also do want to stay away from Standard Chinese as much as possible and teach Written Cantonese. It will take me some time to continue to extract the essence of the language and document it at the core level. Once I've extracted the language it could (and should) be used to create full literary writings in Written Cantonese, and not need to use nor ever learn Standard Chinese. If my target audience is to speak to Cantonese people specifically and not every single person of any Chinese language in existence, then writing in Written Cantonese is enough for my purposes and goals.
I definitely appreciate the feedback :). Thank you!
As a native speaker I assure you that 請 is pronounced differently in context, and that both readings are perfectly Cantonese.
For a more clear example, see 平: 大平賣 ("vernacular" reading; peng4) (lit. big cheap sale; i.e. sale) vs 平面 ("literary" reading; ping4) (lit. flat surface; i.e. surface). peng4 is the "vernacular" reading but used exclusively for meaning cheap. ping4 is "literary" but used everywhere else. "vernacular" versus "literary" is a linguistic classification, but do not necessarily represent either being more common than the other reading. Both readings exist.
I'm happy to hear that both can be used, normally I always have heard more of the "e" shift in a relatively consistent way. I normally say "大減價" for a big sale, but I understand your point was more about showing a demonstration where the "i" may be used. Although I would say that it really depends on the speaker and how they feel. I would most likely use the "e" shift consistently and be perfectly understood.
The example is meant to demonstrate that whether I say 平 as ping or peng changes the meaning of the sentence. It does not depend on how I feel like it.
Another example: I buy some raisins, and the lady gives me some. I say: 咁多！ If I pronounce "gam3do1", I say "That's so much!". If I pronounce "gam3doe1", I say "That's so little!".
(Yes, contrived. Almost always the former is used. But both can be.)
I definitely appreciate the feedback :). Thank you!