I think the problem goes into two directions. In fact, Italy-bound delays stand out during the holiday season, but in my experience the waiting times on normal days tend to be longer Switzerland-bound. Travelling Northbound, I have taken my favorite detour through Chiasso more often than the Brogeda crossing due to queues at the border. Travelling Southbound, the situation was normally well under control.
Essentially, I was asking myself: what might be the reason that Chiasso-Brogeda generally operates at 1+1 for ordinary vehicles, where 2+2 is much more of the rule in Switzerland (and was the rule in pre-Schengen Western Europe)? In each direction, Brogeda operates at one lane for ordinary vehicles and one lane for buses and empty trucks. Loaded trucks are diverted to a separate area and do not really affect the space at the crossing as you experience it from ordinary cars. So why is that? I feel that the configuration on the Italian side plays a role there. First of all, you face those buildings at the Italian side, which cause that there can be only one lane for ordinary vehicles. Unless you remove the separate facility for buses and empty trucks, but I guess that is not really an option for logistical reasons. And then after that, there is the Como Nord exit / entry complex (which is also where loaded trucks re-join the A9) immediately followed by a tunnel. In the present situation, there is little else that you can do but to reduce traffic out of Switzerland to one lane.
So that is why I think that a complete reconstruction on the Italian side might be due. The easy part would be formed by that restaurant right in the middle. Completely removing it would be the easiest option to create a 2+2 crossing for ordinary vehicles, but I think that turning it by 90 degrees would already do the trick. And then there is Como Nord. They should either broaden the tunnel to 3+2 (extra lane in the direction of Milan, to permit a proper merger out of Como and by loaded trucks) or should change its configuration by different means.
But when there is no queue on the Gotthard the queue at the border is much lower (1-2 km?), despite the great number of commuters.
Of course the queues are much longer on days where there are also large queues before the Gotthard. That doesn't have anything to do with commuters, as they tend to pass at different times in the first place, but with the large demand created by tourists. But what I was trying to say is that there there is a distance of over 100 kilometers between Airolo and Chiasso, during which traffic that drip-fed out of the tunnel will reclutter.
Let's say that one car emerges out of the tunnel every 3 seconds. Our of the 20 cars that emerge at Airolo in any given minute, maybe 18 go on to Chiasso. But they will not arrive there in the same minute and in the same sequence as they left the tunnel. On the contrary. Because motorists drive at different speeds, take breaks etc., you may very well cross the border at Chiasso just before someone who did the tunnel half an hour after you. In other words, the bottleneck effect of the tunnel is pretty much undone by the time that you arrive at Chiasso.
Past experience with removing bottlenecks shows that a queue "saved" by a duplication will not automatically re-appear at the next bottleneck. The queues at the Tauern have not simply moved to the Karawanken Tunnel. A Gotthard duplication will probably add some pressure at Chiasso, but not in the sense that a 5km queue "saved" at the Gotthard gets automatically added to an existing queue at Chiasso.