TS:
I agree with you that the role of LE and Special Operations soldiers on active duty are different.
That said, most LE SWAT teams have many former SEALs, Special Forces, Rangers and other Special Operations people on them.
As the SWAT supervisor of my former SWAT team, I had control of who was picked for the team.
I always looked for and picked former Special Operations people first, followed by former Marines, Army Infantry types and last Navy. (Prior military service, was important thing to me.) Combat experience was an added bonus as well.
I think most LE SWAT supervisors try to pick the same type of people that I have outlined as well. On my team, I did have former SF, SEALs, Rangers and USMC Recon. Some were retired from the service with many years of experience in their special Operations units, most with combat experience in various wars, etc.
As of just lately one of the members of my former SWAT team is serving in Iraq, as a SEAL Officer, having been called up in the Navy reserve. I think he has had tours of duty both in Afghanistan and Iraq prior to this tour. There are also many other National Guard (19th SFGA) and Reserve people on the team, that have been called to active duty and served in combat in both places.
So, there is in a lot of cases, fresh combat experience as well as expertise in Special Operations skills within many LE SWAT Teams.
There are Warriors on some, if not most of LE SWAT teams!