Partial pages are counted as there is no clearly defined point when a page is “done”. And in some cases users may have got what they needed before the page has fully loaded so them leaving early is a good thing.
I guess theoretically your scenario could be possible and users get a quick “initial LCP” and then don’t see and later LCP updates and so look better than they actually are. However I think it’s extremely unlikely that the majority of users experience a fast LCP in this way. It’s much more likely that either 1) even that initial LCP candidate is slow, or 2) other intermediate candidates are slow, even if the final LCP candidate is rarely seen. And of course there will be some that fall into 3) and get the very slow loaded final LCP element and time. Therefore I would expect in most cases that such slow sites report a very poor LCP in CrUX anyway.
However, even if your scenario played out frequently, then the early LCP candidate(s) will be the largest LCP that the user experienced. So it is correct to report that as the metric as the largest contentful element seen by the user.
LCP is a heuristic that estimates loading speed and, in most cases, it does a very good job to show that. But, as with any heuristic (or any metric for that matter even if not based on heuristics!), there will be a (small!) number of sites where the metric does not reflect either the best element or perhaps even the user experience. But for our own analysis, and the experience we’ve see since it was launched, those are rare.
Thanks,
Barry