A rifle is better than a shotgun for multiple reasons:
Contrary to popular belief shotguns do penetrate walls if they are constructed of soft material, plus if you are using buck shot that increases the risk of hitting more than just your target. With a single projectile from a small 5.56 rifle you are more likely to hit a target with less risk of over entry than man targets with over entry.
You also have a limited selection of projectiles which include buck shot, slugs, and non lethal ammunition. Non lethal ammunition is good if your target isn't shouldn't at you and is in the open, not so good if they are behind cover with a weapon. Slugs were used when rifles weren't all that common, but a shotgun isn't the best for a long range engagement with a gunman. However a shotgun is like a small cannon, that slug or buckshot fired up close is going to do some ultra nasty damage(trust me unless you want to google what a shotgun wound looks like up close). Projectiles in 5.56 and .223 are small are less likely to severely damage a persons organs, limbs, and flesh. Also remember that all projectiles are lethal.
Police are peace keepers and if lethal force is needed, you don't have to kill the person. If they get shot and fall over motionless, that's when you stop using force. If they are alive, you don't execute them. Instead they are has to be secure for EMTs to arrive and you must be there to record any dyeing words. If they died, well too bad. They shouldn't have committed the crime in the first place or thought about doing the thing that would end up getting them killed.
APCs:
https://www.youtube.com/watch?v=Er7gzj0BbSEhttps://www.youtube.com/watch?v=S3B7iWE1PrAWell good luck getting swat into an area where the badguys can take pop shots at you. Some Departments need them like those with large departments, high violence, lots of gangs. There are also plenty of departments that don't like your small rural towns and areas with low violence.