Now as one caveat to all of this. No item in service is in 100% good condition all the time, and it only takes some half-assed repair job, or a bad bit of weather, and little down time, for rust, or poor craftsmanship, or negligence to damage even a few connected links. This combined with variance in production, and quality of product, could mean that sometimes mail was not what it was meant to be. We have no statistics on equipment failure rates during the middle ages (It would put so many internet arguments to rest if we did) so we can’t know just how often an unexpected blow that should have been blocked became a wound, or possibly a killing stroke. It could be that this failure rate was high enough that these weapons were considered to be worth using against mailed opponents, or that the type of damage accrued was bad enough without the armor failing, for the use of swords and axes to be viable. That said, in a perfect white room scenario, someone in mail should feel secure that a sword will not cut through it, and that even a large axe will struggle to cut them through it.

(Another small aside: First, mail was very form fitting, we see it often depicted as loose and open, but in fact when looking at contemporary sources we find that it was fitted closely to the body. This is likely for ease of movement and to minimize weight. Secondly, mail was not distributed equally across the body, even in a full suit (which there were, dudes just head to toe in chain) the areas most likely to be struck, outer arms, upper legs, chest, shoulders, were thickly armored, with more connections and layers of mail, while other parts had only a thin covering. This is also for flexibility and weight, but also ventilation, layers of metal and padding get HOT. However, this means there are areas on the body, less protected, and so easier to injure with a precise strike. This is where we may see some action with the sword, or spear, and somewhat the axe (though less so as the vulnerable spots are more open to thrusting) and why there is such a mixed interpretation of the viability of some weapons against armour. Also because Hollywood thinks of armor as shiny bulky clothing.

(Another point for axes (Sorry to go on again) is they are cheaper to produce, having only a head, and a wooden pole.)

However… I never specified a time frame. Plate armor has weighed all sorts of amounts through the ages. The Roman army almost never even wore plate, but instead a half plate like described. You take a look at Frigg and she is wearing heavy plate, closer to (as you said) tournament armor. You can also frequently see that she’s wearing a mail hauberk under her breastplate. She’s also frequently using a shield, which appears to be a fair bit larger than a scutum, which on average weighed around 20-25 lbs. So hers might be around 30-35. She’s also wielding a mace with a ridiculously large head and a fairly large haft. It’s not meant for single hand use. So I stand by my comment of 100+ pounds and swinging around a sledge. The one point where you are absolutely wrong is that swords do not cut cleanly through mail.
There are videos and shows (Deadliest Warrior) about people swinging swords, or even the legendary katana, at pigs covered in mail and there is no underlying damage after multiple blows, let alone cutting clean through. There are also videos of axes being stopped dead in their tracks. Sure a good blow will bust open a couple links, exposing more area to strike, but against a new set of mail they are useless.

I don’t count this as an artistic failure. In fact, considering the nature of this comic (a pastiche of WoW), it’d be a failure if they weren’t cartoonishly exaggerated. Now you mention it though, I notice Frigg’s mace does seem to change size between panels 1 and 3.