I suspect some black teas require aging to tame astringent character, either arising naturally from the tea under normal processing conditions, or due to the processing techniques traditionally (Keemun smoked teas, for example) employed for these teas.
Chinese blacks appear to specifically apply here. I have not heard of many Indian blacks that require extended aging periods.
That said, black tea - and very likely other teas, such as oolongs and maybe green tea, too - continues to change in chemistry following cessation of formal processing activity, due to the activation and slow reaction within tea oils and cell membranes components released during mechanical manipulation and heating. In my experience, many oolongs and black teas seem to reach optimum quality in storage long after (one year or longer) batch processing ends.