Ordering a list of objects requires a sort key containing unique values. Sure it could simply be an index number, but a datetime makes much more sense. Although Geocaching does store geocache finds with a datetime object, the time is often 00:00. You can see this if you export and examine your myfinds. The reason geocaching does not store times is historical - in the old days finds were made off line (and many still are, either by preference or simply because the cache is outside cellphone coverage) and so the time the find was logged often does not reflect the time the cache was found. As you have seen, although there is a way to override the date, Geocaching does not support a way to override the time.
As there is no sort key, there is no guarantee that a query on the Geocaching database will return the caches in the same order. This is an intentional feature of databases - they are optimised for speed. If you don't ask for the data to be sorted then the database will use any tricks it can to get the data to you faster, even if it means that the data is out of order. An example of how this might happen is that when someone runs a query that includes some of your finds (eg all caches in an area), these will be cached in the server so that when you subsequently run a query on your finds those results may be returned earlier in the query. Another example of this is the MyFinds query - the contents of this gpx file is not even sorted by date. And this is also the reason that Geocaching supports the override of milestone finds.
As Geocaching does not store, and therefore export, find times, and as they do not store any index (eg nth find that day), it makes sense that Project-GC should not attempt to order finds beyond the date either. As was mentioned in other posts the order of unsorted data in Project-GC is also undefined and not guranteed to to be the same over repeated queries.
Geocaching has often been requested to store times, especially now that cellphones have become the primary GPS tool. Every time though, there is a large body of people requesting that this not happen, and it is also unclear how the currrent body of finds should be handled (all found at midnight?).
I do know that the API that Project-GC has access to for lab cahes is very limited, even missing other data that we would like to have (eg coordinates, owner). I would expect that Geocaching does not store times for these either. If Geocaching did store times and make these visible through the API Project-GC would use them.