I'm going to write some stuff which is probably mostly true but represents a game designer's understanding, not expert knowledge.
SWAT teams may storm a building with armor on their arms and legs, a person in front with a shield, and helmets with face masks. Soldiers in the field will usually have none of this equipment. The difference is not a matter of the military being cheap, especially for the US Army, which spends exorbitant amounts of money on training and equipment, and would gladly invest more if it were of benefit. The problem is that the military has conditions to deal with that make the equipment less useful. The general answer for "why doesn't the military use more personal armor", including personal ballistic shields, is always some combination of:
1. It is too hot, heavy, and/or bulky,
2. It doesn't reliably stop the threats they expect to face.
Either of these can be solved, but only by trading off heavily against the other. The more gear soldiers wear, the more quickly they tire out in the field, so if they aren't expecting combat, they'll usually only wear armor sufficient to cover their vital organs. If they are expecting combat, they'll have more coverage, but still won't wear armor for their arms, legs, or face, even though such armor exists.
SWAT teams can do things differently. They have the luxury of having short, relatively predictable missions. They are in friendly territory, and can expect only a single hotspot of action. Unlike the military, they expect to be attacked primarily with shotguns and handguns. Shotguns increase the value of face coverage and full-body shields, and both shotguns and handguns can be stopped with relatively lightweight armor. SWAT teams also dictate the pace and timing of their engagements, and they are unlikely to be flanked, thereby increasing the value of the directional cover a shield provides. In addition, their targets are usually a handful of isolated self-interested criminals, who lack ideological convictions; SWAT teams therefore benefit disproportionately from the sheer dehumanizing shock factor of storming a building with face masks and a shield. Criminals usually don't want to be martyrs.
The military, on the other hand, needs mobility and flexibility, and faces threats that are hard to stop with lightweight armor. Infantry training foregoes carrying shields in favor of using vehicles and environment for cover. Assaulting buildings is more dangerous, but they can sometimes use explosives to nullify this problem, and other times they hand off the job to specialized teams with specialized equipment. Finally, modern military campaigns, especially for the US, often involve the threat of civilians being alienated and becoming hostile. Under these circumstances, a human face to the troops is likely to protect them from more harm than an imposing shield will, or a face mask that makes them look like a faceless stormtrooper.
As for an in-game implementation, I think any system for ballistic shields in LCS should respect the main tactical use of them -- one squad member providing cover for others behind.