
The chainmail bikini is ridiculous, plain and simple, but it's not just in how ineffective it is, rather that it's something worth discussing at all. It's a subject that, while it may seem simple and obvious at first, can get quite detailed and technical. First off, however, what is a 'chainmail bikini' in the first place? Simply put, it's a suit of armour or outfit worn to protect a character that doesn't actually protect much and, instead, provides fan-service. While this most often happens to female characters it does, on rare occasion, happen to men, as well. Most noticeably, however, is that the armour is utterly impractical and/or ineffective, but it's a bit more.
Here's the thing. Historically, if you wore armour and wanted it to be practical, there was really only one way to go. Be it male or female, the full suit of chainmail/plate was practically required for 'full protection.' Due to the way these things are made, they are mostly unisex. A properly created outfit simply covers everything and is unlikely to fit a character's form. A female character wearing one of these suits would be indistinguishable from a male unless she spoke or removed her helmet and, if her voice was low/gravelly enough and/or she had cut her hair, even then it would be difficult to tell. Needless to say, this is very uninteresting to look at and quite boring. This sort of outfit is what NPC soldiers who are often killed off en masse wear and not main characters.
Why not embellish a little, then? It doesn't have to be entirely 110% realistic and practical; just enough to look the part. The thing is that even here it doesn't really work. One of the best ways to distinguish characters is by their outfits and, for females, this often ends up making it obvious that, well, they are female. In doing so, a quirk of armour comes into play. Make it form-fitting and, suddenly, either girls have massive metal bands across their chest, just below it, or armour that's form-fitting. It's just part of how outfits work. The same applies for men, as it often results in a reduction of armour in the chest and belly area, two of the most vulnerable areas in an actual fight due to their size. Gauntlets and leg-guards may or may not be part of the outfit still but, at this point, they are drastically reduced in efficiency since the easiest part of the body to hit is now entirely vulnerable.

Of course, when the characters are basically wearing just outfits, this becomes a bit less defined. Each character has its own unique style often associated with it in games, which, in turn, results in the notion of protection becoming secondary. In the grand scheme of things, despite wearing a single-piece, skin-tight outfit, Celes from Final Fantasy VI is actually more protected than Cloud from Final Fantasy VII simply because she has a whopping two shoulder pads to his one. Wakka in Final Fantasy X is the most heavily armoured of the protagonists simply because he has a shoulder pad, even if it's half falling off. Everyone else, male and female, may as well be walking around naked, as far as armouring is concerned. This results in a strange twist in which the chainmail bikini is actually a step upwards in terms of protection.
Thusly, the inherent problem with the chainmail bikini is revealed. While it certainly is possible to wear protective armouring that is entirely practical, this armour is not what a main, or even supporting character, would typically wear, and with each step made to distinguish themselves more, there is almost certainly a reduction in practicality for both men and women and, for women, almost certainly a rise in fan-service. Even among the practical sets there is often an inherent amount of fan-service and reduction in practicality. In League of Legends, for example, the character Leona may, at first, appear to be very practically dressed. She is clearly at least partially heavily armoured and carries a thick shield. However, her head gear alone reveals that this is an impractical outfit as, in a serious fight, not only does it not protect but it provides ample hand-holds for a foe. Even if we were to assume the golden parts of her armour to be plate and the darker parts to be mail, the placement reveals that the outfit has sacrificed practicality for appearance and, given that she is clearly capable of moving her torso despite the outfit being form-fitting, it is unlikely that this is plate as we know it. The combat skirt is also fairly impractical since, once again, even if it's armoured, it drastically increases the amount of weight that she would need to carry into battle simply because she opted for a skirt instead of more practical wear.

By comparison, Lux's outfit, despite being a squishy mage, is far more practical. Offering increased torso protection and, most importantly, ditching the skirt for armour more moulded to her form, she can reduce the weight she carries immensely. However, this still leaves her belly exposed and any blows to her upper torso would be deflected towards the centre of her chest as opposed to away from it, making things much worse for Lux in a fight. This is not to say in any way that this is done for fan-service but, rather, to accent the problem. As outfits get more and more personalised, this results in a reduction in practicality and, for female characters, this can so easily lead to the chainmail bikini.
In the SoulCalibur releases, most of the cast, male and female, does not wear armour. The one female character that does, Hilde, wears an outfit that is actually very practical, with armour that covers the majority of her body while still allowing for movement, full protection through and through, and so-forth. However, it's still not a full suit of plate armour and, in battle, would have key weaknesses; for example, her stomach is only protected by a plate piece that protects her upper torso, as well as what appears to be a separate piece of armour upon her belt. This leaves gaps to be struck and vulnerable points. Even if her red outfit is mail, as opposed to cloth, this is still a weaker point. Once more, with the armour formed to her chest, blows are deflected towards the centre, although in a much lesser way. There is no doubt that this is practical and acceptable to wear in combat. However, when compared to Siegfried, there is little doubt as to whose armour is more practical and whose is more fanciful.
The point here isn't to mock, shame, or insult female outfits in games, however, but rather to highlight an inherent problem and discuss why this trope so often arises, even unintentionally. Practicality is hard to achieve, and doing so while giving each character personality is an insanely difficult task. Every increase in personality results in a decrease in practicality.