None of the style guides I'm familiar with have anything to say specifically about why e.g. or i.e. shouldn't be used.
(Most do suggest it's better to use full words, especially in any kind of formal writing. I find this somewhat ironic, since it's people who read formal text who are more likely to understand the correct usage of i.e. and e.g.)
However, the UK Government actually does provide a few justifications:
‘eg’ can sometimes be read aloud as ‘egg’ by screen reading software. Instead use ‘for example’ or ‘such as’ or 'like' or ‘including’ - whichever works best in the specific context.
‘ie’ - used to clarify a sentence - isn’t always well understood. Try (re)writing sentences to avoid the need to use it. If that isn’t possible, use an alternative such as ‘meaning’ or ‘that is’.
(Note that in the UK it's not uncommon to see the abbreviations used without periods.)
While the explanation given for avoiding e.g. might sound "stupid" to some people (there are many such comments in response to the government's style decision at the end of the linked web page), it at least is a reason—regardless of such debate.
The reason given for avoiding i.e. seems to be more applicable in general—it's simply not "always well understood."
Personally, I continue to see confusion over the use of e.g. and i.e. I wouldn't be surprised if at least part of the shift away from using the two-letter forms is to avoid their misuse. (Although that's just speculation, since no other style guides I'm aware of mention that specifically.)
However, the use of these abbreviations is probably contraindicated by a growing style of writing called plain language, one in which it's preferable to use words and syntax as simply as possible while still retaining the meaning of what's being communicated. Everything being equal, if nobody is confused by for example or for instance, but some are confused by e.g. or i.e. (or, even if they're not confused, it takes them a bit longer to parse sentences with the abbreviations), then it would be beneficial to a general audience to simply avoid the abbreviations.
There are certain conventions of style that are commonly followed, but specifics depend on particular style guides.
According to The Chicago Manual of Style (6.51), for instance, the initial example that you gave in your question is incorrect because
in formal writing, Chicago prefers to confine the abbreviations i.e. (“that is”) and e.g. (“for example”) to parentheses or notes, where they are followed by a comma.
Which would mean that your sentence, according to Chicago, should be rephrased as something like this:
This parallel composition can be transparently split between two cores, allowing several benefits (e.g., faster execution).
Note that in order to get e.g. inside parentheses with an example I had to shift things around slightly (and add some words). This stylistic guideline will "force" certain sentence structures that would not be required with the actual words for example.
Also note that there are some actual rules of grammar (not style) that preclude e.g. from being used in every place that for example can be used—but you provide links to those discussions in your question. (For instance, the first link explains why I had to give an item after e.g. in my rephrased version of your sentence.)