Actually, the task is to retrieve downed air crew and otherwise perform combat search and rescue functions. So these craft often were behind enemy lines making the pickups. They also had some support in this endeavor. In this sort of situation, they were exposed to a lot of risk, but these were extremely brave, badassed airmen. HH-3's had a lot of range on them and they were faster than Hueys, despite the size. They're armored in key points, including cockpit and engines, which means they are more survivable. There's a number of factors why they are the go-to for CSAR operations in this era.

The CH-53 (or HH-53B's, which are phased in later 1967 and start operating immediately in Southeast Asia) has more speed, which is why they are phased in. They also have more armament for suppressing the enemy on the ground while performing these duties.

For example:

"Due to the nature of combat operations, particularly in Southeast Asia, many of the operational H-3 crews received honors and awards. The highest American military award, the Medal of Honor, was awarded to Captain Gerald Young, USAF, on 9 November 1967. Young piloted an HH-3E, AF Ser. No. 66-13279, of the 37th Aerospace Rescue and Recovery Squadron in an attempt to rescue a US Army Special Forces reconnaissance team trapped by enemy fire in Laos. When his aircraft was shot down, he escaped the burning wreckage and, despite severe wounds, evaded capture for 17 hours until being rescued[8]. Six men were aboard 66-13279 when it went down just after midnight on the morning of 09 Nov: four aircrew from the 37th ARRS (Young, Capt Ralph W. Brower, SSgt Eugene L. Clay, and Sgt Larry W. Maysey) and two wounded recon team members from Command & Control Central, MACV SOG (MSG Bruce R. Baxter and SGT Joseph G. Kusick). Late on 09 Nov Captain Young was recovered and a four-man recovery team inserted into the crash site, but darkness precluded a detailed search of the wreckage. On the morning of 10 Nov, three charred remains (two crewmen and Kusick) were removed from the wreckage and placed with MSG Baxter's remains about 40 meters from the wreckage (Baxter had been thrown clear) to permit recovery by a single hoist. However, a combination of weather and renewed enemy action forced the recovery team to leave the crash site without the recovered remains; although the recovery team was picked up safely, the four remains could not be retrieved. The remains of the third aircrewman were not found. "