I'm curious. Exactly why does any law enforcement officer require sub-sonic ammunition to use against the people it protects and serves?

What about a series of staged ignitions, built into the bullet head, so that the bullet is continuously propelled forward but at a subsonic speed?

Try tiny bullets at much higher speed. That should get them in beneath the human hearing threshold and improve range and accuracy.

Why not just use Silencers ? And there ARE Silencers on Guns other than subsonic hand guns.
http://www.silencerresearch.com/sound_suppressors_on_high_powered_rifles.htm

Flink, nowhere in this article does it mention law enforcement. The article is purely about a military round for Spec Ops use. However, the police could use such a round when doing raids on drug houses, etc. where there are heavily armed potential assailants that could be taken out silently as to not give the other bad guys (victims, as you would probably call them) an audible cue to take up arms. Protect and Serve by taking out or arresting those that do the opposite, i.e. criminals.

@ Estelja. Re: Nowhere in this article does it mention law enforcement. The last para of the article states: "Dual use by law enforcement is an additional SOCOM goal."

@estelja:
Last paragraph, third sentence:
"Dual use by law enforcement is an additional SOCOM goal."
US LEO has neither a requirement nor the authority to use anything other than flash suppressors. It's not legal to simply shoot a target unless a hostage or other LEO is about to be shoot by said target. I'm not arguing that it wouldn't make things easier, just that it's not legal.
It's not easy to approach a building unseen nowadays. There are dozens of IR surveillance/security cam systems on the market and they're fairly simple to build from scratch.
Covert entry is seldom practiced in a civilian setting unless there are hostages. Entry into most buildings is accomplished with brute force and plenty of noise. There's no way to do it in silence. At best, you might quietly divert the DWV into a bucket in a crawlspace or capture the outflow to the sewer line before entry so that you don't loose evidence. Once the ram hits the door, there's no need for silence.
Stealth is often practiced but seldom used. It's mainly for building clearing when the environment is mixed (target/friendly) or unknown, and then only when a surreptitious entry is possible. A locked and chained door usually makes that impossible. And it's good practice for the period after the entry if you're working a large, multi-floor building. There are few things that suck more than having someone shooting at you through the floor/ceiling.
UK LEO have access, but only because they have so often had to deal with many flavors of terrorist organizations.

If you want it to be effective at long range and subsonic you have to throw a large heavy bullet (I would recommend some on the order of 60cal.) or have an engine on the bullet. (firing little magnesium or white phosphorous fueled ramjets would be cool.

300 AAC/BLK Does this now with a 220 grain 308 bullet at just over 1000FPS. Works in an M4/AR15 with the swapout of a barrel. Uses standard M4 bolt and magazines. Done
http://en.wikipedia.org/wiki/300_AAC_Blackout_%287.62%C3%9735mm%29

silencers and suppressors are the same thing. They only mute the sound at the barrel, not the second crack from the supersonic bullet. To be effectively silenced the ammo needs to be subsonic