US Chess rule 16B2a, and the two rules that explain it
[ Claude wrote all of this. I think it's good stuff - but, treat with care! -Trevor ]
A tournament chess clock is required to be silent, and the ban is explicit that it covers a low-time warning, not just the flag itself:
Digital clocks must be set to produce no sound. This includes, but is not limited to: beeping when a player has run out of time in the final time control; beeping when a player reaches the end of any time control; warning beeps to indicate a player is approaching the end of a time control; and beeping when a player presses the clock. A digital clock that can be set to produce no sound is preferable to a clock that cannot.
US Chess, Official Rules of Chess, 7th ed., rule 16B2a (Sound)
Under US Chess rules, running out of time does not end a game. A player has to notice and claim it, and nobody else is permitted to help:
Only the players in a game may call attention to the fall of a flag; it is considered to have fallen only when either player points this out. A director must never initiate a time-forfeit claim. Spectators, including players of other games, who point out the fall of a flag in any manner, may be disciplined by the tournament director to the point of expulsion from the playing room, loss of their own games, or expulsion from the tournament.
rule 13C1 (Only players may call flag)
No one, except a player's opponent, may call that player's attention to the fact that a flag is down, the opponent has moved, or the player has forgotten to press the clock after moving. These prohibitions also apply to the director.
rule 16Y (Assisting players with time management prohibited)
That is the whole argument. A beeping clock announces the flag to the room, which is precisely what a spectator can be expelled for doing and what the director is forbidden to do. A warning beep is worse: it is time-management assistance, delivered before the flag, to the player losing the race. The rule is about keeping the clock from making the claim.
Noise is not what the rule is aimed at, but it is a real benefit and worth saying out loud. A hall of silent clocks is a much quieter room than one where several dozen machines are chirping through everybody's endgame - and in a long tournament that quiet is worth something on its own, whatever the rulebook was thinking about.
The same rulebook notes the contrast in a TD Tip: "Remember in FIDE competitions the arbiter can call the flag, and should do so." Once an official is the one who calls time, a clock that announces it is redundant rather than illegal, and FIDE's equipment regulation asks only that an audible alarm have a setting to switch it off.
Go inherited the opposite convention. Byo-yomi has been counted aloud by a timekeeper for as long as it has existed, so an audible clock is idiomatic rather than suspect, and Go clocks ship a low-time warning as a feature. Same hardware, opposite answers about whether the equipment may tell you what it knows.
But what has changed is the time control itself. Byo-yomi is legacy now. Many US Go tournaments have moved to Fischer (bonus) time, and every tournament I run uses it: the New England Open and the Mass State Championship are 40 minutes plus 15 seconds a move. That changes the calculus, because the tradition that made an audible Go clock respectable was byo-yomi being counted out loud. Under Fischer there is nothing to count. There is no overtime period, no timekeeper, no ritual reading of "nine, ten" over your shoulder. Main time simply runs down, and when it hits zero the game is over on time, exactly the sudden-death situation chess is regulating. A warning beep in that setting is not an echo of an old custom; it is a machine telling the player who is behind on the clock that they are about to lose, which is precisely rule 16Y's "assisting players with time management."
So the Go answer can no longer be settled by pointing at the byo-yomi tradition. We have adopted the chess time control, and the question of what the clock is allowed to say has to be answered on its own merits.
Here is the part I have lived through. Two years ago I lost a game on time because I had not turned the sound on correctly, and at this year's New England Open the same thing happened to two more players. A clock that is expected to beep is a clock whose silence gets read as working equipment, right up until someone's flag falls unannounced.
That is the practical case for the chess convention, and it is a director's case. When nobody expects sound, a misconfigured clock can never be blamed for failing to make any, and the TD's job gets much easier. It is always heart-breaking to have to tell a player: "I'm sorry that your clock did not make sound, but it's your responsibility to ensure that your clock is functioning properly. Therefore, you lose on time." A rule of silence removes the whole conversation.
Which leaves a live question for our own events, and it is the reason this page exists: should the clocks in a Go tournament warn you before your main time runs out? There is a real case on each side - the help of a warning against the quiet of a silent hall - and it is on the New England Open player survey.
Source: US Chess Federation's Official Rules of Chess, 7th edition (online-only edition, 8-24-20), chapter 1. Quotations verbatim.