THE DECISION of Assistant Attorney General William F. Baxter to pursue vigoriously the goverment's antitrust case against the American Telephone and Telegraph Company suggests Mr. Baxter may be ready to enforce the antitrust laws more aggressively than are many of his associates in the Reagan administration. That's the good news. The bad news is that this decision leaves the future of AT&T and, hence, of the entire communications industry where it should not be: in the hands of the federal courts.

The AT&T case has had a long and highly emotional history because the stakes are so high. Never content to be just a collection of regulated telephone companies, Ma Bell has been moving into many other aspects of modern communications in an era in which the whole realm of message dissemination is undergoing change: radio, television, satellites, computers and so on. Other companies in the field, with justification, fear the economic power of the Bell System. It' size and the strong financial base its telephone companies provide make it an awesome and, actually or potentially, a predatory competitor.

Mr. Baxter believes the appropriate solution to this problem is to split AT&T along the lines of actual competition. It would still control, for example, the operating telephone companies that hold monopolies in the communities they serve. Many other activities would be spun off into other companies. Unfortunately, the line between which of AT&T's operations should be regulated monopolies and which should be competitive is not as clear as it once was and seems to grow dimmer every year.

One can argue interminably over these matters, as the lawyers for AT&T and the government have done for several years. Ideally, that argument would be conducted -- and concluded -- in Congress, the government body that ought to decide such major questions about so vital an industry. But since Congress is unable or unwillingly to do its job, despite a valiant effort by some members in the last session to focus attention on this matter, the burden of decison-making has once again been tossed to the legal system.

In that situation, the Department of Justice had to apply the only standards Congress has provided -- the murky words of the antitrust laws. Once the issue was joined, the best solution would have been a negotiated settlement. But the only settlement on which the lawyers could agree was one Mr. Baxter found to be too favorable to AT&T. Believing that, he had no choice but to pursue the case vigorously and reject the request of Secretary of Defense Caspar Weinberger that it be dropped.

The courts are not expecially well-equipped to decide the kinds of questions this case raises. But, as in reapportionment and school desegregation, they are the best available alternative when legislatures fail to do the jobs that are rightly theirs.