Common Errors: my mistake!
Hmmm... I should maybe reread my posts more before publishing, because in another article I said "we should be paying close attention to the thought processes behind this change and trying to make the way we right English match the way we speak it" and then forgot to describe the process in any detail.
Because even though the solution I proposed was to legitimise the writing of contractions, this is not the internal process causing the change. If the average speaker's internal model saw 've as a contraction of have, then no-one would make the 'mistake' of using of instead.
Put it this way: the "error" only occurs when have is used as a second auxiliary -- no-one would say *I of done it in place of I've done it/I have done it, for example.
So it would appear that here we have ceased to think of 've as an verb at all, let alone an infinitive. At best it is a clitic that modifies the first auxiliary to make it part of the perfect construction, but in fact it would appear to me to be in reality a new suffix, because I cannot see any situation where you could syntactically separate 've from the first auxiliary.
What we see here is English gaining a new fusional feature, and while English has displayed a tendency to become more isolating over the centuries, it isn't unknown for a language to pick up new fusional elements even when the general tendencies is towards isolation.
Consider, Latin vs the Western Romance language family.
Latin was a highly fusional language, and relied on very few periphrastic constructions. However, the future was a periphrastic form, consisting of the verb in the infinitive followed by the present indicative of to have -- so I will do was literally formed as to-do I-have.
Most members of the Western Romance family has lost a lot of the fusional features of Latin, but at the same time, the future has mutated into an inflected tense, with suffixes derived from (and in some cases identical to) the present tense of to have added to a future root that is almost identical to the infinitive.
Note that the creation of these new suffixes didn't alter the present tense of to have in any other constructions, even though in the early stages of this change, grammarians would most likely have declared that it was "obvious" that they were the same thing, and lamented the "common error" of people saying nous le ferons instead of the previous nous le faire avons. But today, the latter looks so unnatural that it would not be understood except by a scholar.
This is analogous to what I believe is happening in English. One particular usage of the verb to have is becoming replaced with a suffix derived from, but not identical to, a form of the verb. However much the status quo appears more logical, the frequency of occurrence of the "of" error (Google "would of", "could of" etc, and you get millions upon millions of hits) tells us that people's brains just don't work that way.
You cannot rewrite how people pick up their native language. People seem to pick up 've as a suffix, not an infinitive, so it's time to stop resisting. While it would be natural for a suffix to be incorporated into the word without the apostrophe, that would be a step too far for most pedants, and even besides that would be a fairly radical change that would take a bit of getting used to.
So I advocate using the contraction notation for now, but recognising that it has now ceased to be a contraction in the mind of the native speaker.