It seems to me that the CBS Television Network made a grievous mistake when it announced that Dan Rather would succeed Walter Cronkite as King of the Evening News.

With all due respect to Mr. Rather, for whom I have nothing but admiration, I believe that the question of Cronkite's successor was far too serious a matter to be left to the network generals.

The American people should have been given the opportunity to vote for the person they preferred to take the seat of "the most trusted man in America."

A TV anchorman holds one of the most delicate and powerful positions in any country. Every nation chooses one differently. In England when a BBC anchorperson abdicates, the title is passed on to the eldest son. If the anchorman has no children, it goes to the nearest blood relative.

In Rome, the Italians choose one differently. The head of Italian television calls together the College of Commentators, who meet secretly in a studio in the basement and cast their ballots. When white smoke pours out of the TV station's tower, the millions of people in the square start screaming, "Viva il presentatore," and the new anchorman is carried in his glass news booth through the streets of the city.

Soviet television never announces in advance when it is changing its anchorman. The only way people know is when they turn on their sets for the 7-o'clock news and see a new face on the screen. No mention is made about what happened to the previous anchorman, and nobody in his right mind would dare ask.

But in the United States, we do not have a precedent for choosing a new TV anchorman. The reason for this is that no one, including the Founding Fathers, ever imagined that anyone but Walter Cronkite would give the country its news.

Since the position of the CBS anchorman has now become the highest office in the land, the only democratic way of selecting Cronkite's successor would have been to allow those seeking the job to run for it in a nation-wide election.

CBS could have easily done this by holding primaries in each state and whittling down the candidates until there were only two left by November.

The candidates should have been given free time to allow the American people an opportunity to decide who was best fitted to bring them the grim tidings of the day. They should have been tested in the public arena as to how they would handle the news of wars, pestilence and inflation. They should have been evaluated by the TV viewers to see if they had the moral and physical strength to tell it straight without regard to personal prejudices and special interests.

And, finally, they should have been required to debate each other so that the public could judge how they compared with Cronkite for grace and serenity under pressure.

The people, not CBS, should have been the ones to determine which anchorman they would trust to have his finger on the control-room button.

I am not saying that Dan Rather will not be a worthy successor to Cronkite. All I'm claiming is that, under our system of government, the selection of a TV anchorman should be decided by ALL the people.

U.S. presidents may tell you the truth -- or they may not, depending on how the political winds are blowing. But the man who anchors the CBS evening news is the only one required under oath to swear to the American people every night, "And that's the way it is."