Steam is not neutral
The vapour coming off a brewing vessel is not only water. It carries the volatile aromatic compounds that are the fastest-moving part of what has just been extracted, and once they are in the room they are not in the cup — the pleasant smell filling the kitchen is a measurable loss rather than a bonus. That is the basic case for a lid, and it is stronger than it first sounds, because those volatile compounds are a disproportionate share of what makes a good tea recognisable. They arrive first in the nose, they set the impression before anything is tasted, and they are the part that distinguishes a fine example of a tea from an ordinary one. An uncovered vessel is running an extraction and a simultaneous slow loss, and the loss is concentrated on exactly the fraction that is hardest to replace.
The heat argument, which usually matters more
Evaporation removes energy, so an open vessel cools substantially faster than a covered one — for a delicate tea steeped for three or four minutes in a small pot, the difference over the steep can be several degrees, which is enough to move it out of the band it was meant to be in. Whether that is a problem depends entirely on where you started. For an oolong or a dark tea that wants sustained heat, an open pot is losing precisely what the tea needs and the lid is doing real work throughout the steep. For a green tea in a mug filled with near-boiling water, the same cooling is quietly helping and covering it would remove the accidental correction. Covering is therefore not a general rule to be applied everywhere but a decision about which direction you want the temperature to move during the steep, and it should be made with the rest of the setup in mind.
Where covering goes wrong
A covered mug with the leaf still in it, left to stand while you do something else, is the recipe for a stewed cup: full temperature maintained, extraction continuing unchecked, nothing removed at any point. The lid is not the underlying fault there, but it makes the underlying fault considerably worse, and the common advice to cover a mug is given without the accompanying instruction to take the leaf out on time. The same applies at a larger scale to a lidded pot left on a warmer for an hour, which holds the leaf at temperature and produces something harsh and simultaneously flat — the worst of both directions. The lid helps during the steep and hurts after it, and those two phases are almost never distinguished in the advice. Cover while brewing, uncover when the leaf comes out, and never cover a vessel that still holds leaf and is going to sit.
The gaiwan lid as an instrument
In short-steep brewing the lid does several jobs simultaneously, which is why the gaiwan can get away with having no filter. It holds the leaf back during the pour, its angle controlling how fast the liquor comes out. It closes the vessel between infusions, keeping both heat and aroma in during the interval where a session loses most of both. And it is the standard tool for reading a tea: lifted and smelled while still hot, it carries a concentrated sample of exactly the volatile fraction the vessel is currently holding, and it reports on where a session has got to more reliably than the liquor does. That last use is the reason experienced drinkers appear to spend more time with the lid at their nose than looking at the tea, and it is a habit worth copying — it costs nothing and it is the fastest available feedback.
Cold and iced preparations
The argument inverts at low temperature. A cold brew is sealed for hours, and the reason is straightforward: there is no steam to speak of, so the closure is about keeping the refrigerator out of the tea rather than keeping the aroma in — an open jug of cold-brewing tea will pick up whatever else is in there within an hour or two. Flash-chilled iced tea is the interesting case. The brew is hot, so the volatile loss is real and rapid, but the entire point of pouring immediately over a full measure of ice is to capture those aromatics in the finished drink before they can leave. Speed does the job a lid would have done, and does it better. Covering the pot during the ninety seconds of the brew is still worth doing, and costs nothing, but the ice is what makes the method work.
A practical position
Cover during the steep, uncover when the leaf comes out, and never cover a vessel that still contains leaf and is going to stand for any length of time. For teas whose appeal is fragrance — floral oolong, scented green tea, good white tea — the lid is worth being deliberate about, and the difference between a covered and an uncovered steep is easy to demonstrate to yourself with two mugs. For a robust black tea that is going to take milk, it makes very little difference either way and is not worth thinking about. And if a mug has no lid, a saucer is a lid: the effect is not sensitive to what the cover is made of or how well it fits, only to whether the vapour is being kept in contact with the liquid or sent into the room.