t excluding the cost of owned housing from official CPI artificially depresses it.
That may be true. But there is no good way of putting in owned housing. I am not well read on the literature, but I remember going to a seminar or two on the issue. Apparently, there are many ways of doing it, and all of them are wrong
And, then, in any case, many people (I mean, economists) claim that CPI is overestimating the true inflation, by not accounting well for technological improvements. If definition of CPI is touched, chances are more people will argue that it should be done in such a way that published inflation numbers will be lower, not higher.
I would argue in this case that CPI is measuring CPI. Whether it is "true" inflation or not is an impossible question, because there is no "true" inflation that can be represented by a single number. The reason we care about CPI is that it has been measured for a long time, giving us possibilities for intertemporal comparisons: if CPI is up, inflation is up. Absolute reported number should not be taken as seriously.
Obviously, for different people/industries that "true" inflation is different. Ideally, things like pensions would be adjusted using not CPI, but some version of it, that takes into account spending patterns of retirees. However, creating such an index would imply opportunities for tinkering with it - and governments would have all incentives to tinker it down. We are safer using a well-established series, like CPI.