Even if it couldn't have been done during American air raids for fear of blue on blue incidents, it seems like it would have been a good way to hamper NVAF training or routine patrols.
There's two main reasons: North Vietnamese aircraft avoided the U.S. Navy's SAM-armed ships, and the U.S. Navy rarely put its ships close to shore. Also, the Navy shot down more than three MiGs with SAMs. Read on.
Let's talk about the missiles, first. During the Vietnam War, the U.S. Navy had three predominant surface-to-air missiles, usually called the "Three Ts." These were the Talos, the Terrier and the Tartar.
The Talos was the big, long-range missile. It usually showed up on the few ships large enough to carry it. These were rail-fired missiles, functioning a lot like a gun turret on a World War II battleship. The rail would hold the missile, and after firing, the rail would have to be reloaded just as if it were a gun. The Navy did retrofit some of its WWII cruisers into guided missile ships, replacing a turret or two with Talos launcher(s). The Talos had a lot of variants with a lot of different ranges, but the longest kill on record was a drone shot down by the USS Chicago at a range of 96 miles in 1967.
The Terrier was the medium-range missile. It could be found on smaller ships that didn't have the space for a Talos setup. As with the Talos, there were several variants with different ranges, but 30 miles is a good ballpark figure to consider.
The Tartar was the short-range missile in the T family, with a range of less than 20 miles. It was a shortened Terrier and didn't have any combat action that I could quickly find in Vietnam.
Now that we've talked about the missiles, lets talk about where those missiles went.
Most of the U.S. Navy combat you read about involves strikes from aircraft carriers based at Yankee Station (officially, Point Yankee), about 100 miles east of Da Nang. The exact position varied, and I'm just giving you a general location, since Yankee Station isn't what we're going to talk about. (If you want to read about it, try On Yankee Station and Tonkin Gulf Yacht Club, both by Naval Institute Press.)
What's important to you is a place called PIRAZ Station. PIRAZ stands for Positive Identification Radar Advisory Zone, and during the Vietnam War, the U.S. Navy stationed cruisers, frigates and destroyers on rotating patrols at a point about 30 miles off the coast of North Vietnam. From this point, the radars aboard these ships could sweep across North Vietnam, directing U.S. Navy bombers and fighters wherever they needed to go. If an attacking aircraft was inbound to Yankee Station, that aircraft would first have to fly over PIRAZ Station or deal with the U.S. Air Force over South Vietnam.
David Boslaugh, author of When Computers Went to Sea, the Digitization of the United States Navy, writes quite a bit about how the need to coordinate fighters and bombers over North Vietnam led to improvements in combat control systems aboard the U.S. Navy if you're interested in that.
Relevant to our topic, though, he also discusses how the Navy's CIC improvements allowed it to better intercept North Vietnamese aircraft with SAMs.
Now, thanks to radar detectors, the North Vietnamese knew the Navy was out there, and they also could tell what missiles were out there, based on what radars were broadcasting. On May 23, 1968, the USS Long Beach became the first U.S. Navy ship to shoot down an aircraft with a SAM, as it used a Talos to blow up a MiG over North Vietnam. To do so, it had to employ a bit of trickery.
Ships at PIRAZ Station usually spent about a month on duty before rotating south. On this occasion, Long Beach made a big show of departing, talking to its replacement over the open air and apparently steaming south. The next night, the Long Beach steamed back north under tight emission control ─ no radars showing.
The replacement destroyer was armed with shorter-ranged Terriers, and the North Vietnamese believed they were safe to fly. Instead, the Long Beach lit up its radar and destroyed one MiG. Later that year, the Long Beach destroyed another MiG, but I don't have a source as to how.
For most of the rest of the war, the North Vietnamese stayed well away from the U.S. Navy's surface ships. Toward the end of the war, as the North Vietnamese began to win, that started to change.
In 1972, the U.S. Navy launched a mission to mine Haiphong Harbor from the air. With fighters providing aerial support, the mining aircraft were also backed up by the cruisers Long Beach and Chicago. When North Vietnamese aircraft attempted to interfere, the Chicago launched its Talos missiles, destroying a North Vietnamese attacker.
Now, those are the three SAM kills you asked about, but there are others ...
On July 19, 1972, five MiGs attacked the USS Biddle in two raids while it was at PIRAZ Station. In the first raid, the Biddle destroyed one attacker with a Terrier missile. In the second, according to the ship's records, another aircraft was destroyed with a blast from gun batteries. The Biddle suffered no damage.
A few months before the attack on the Biddle, the North Vietnamese launched their first airborne attack on the U.S. Navy during the war. On April 19, 1972, American ships were bombarding coastal positions in North Vietnam. The Vietnamese reacted by sending MiGs and missile boats after the American ships. One MiG scored a direct hit on the destroyer USS Higbee with a 250kg bomb, and the cruiser Oklahoma City was damaged by fire from shore. The USS Sterett, meanwhile, shot down one attacking MiG with a Terrier.
In conclusion, the North Vietnamese knew the U.S. Navy's limitations and stayed well away for most of the war. The U.S. Navy did not want to risk its ships to unnecessary danger, and the North Vietnamese were reluctant to engage the U.S. Navy except close to shore, where it did not usually venture.