There is some merit to this.
Speaking as a TD for OTB tournaments, I will go after idiots (usually turn out to be kids) who make repeated draw offers to distract or just plain disrespect the opponent, especially if they are clearly lost. 1 verbal warning and then I start docking time off their clock.
Hi, Jay. I think it would be a good idea [for all game types here, in fact] to include the provision for all draw offers to be clearly indicated within the 'moves box', especially for tournament-type games. I believe if I'm correct, standard OTB-type chess does not allow for a [subsequent] draw offer to be proposed by a player if their opponent has not previously offered one themselves.
It is not only somewhat annoying [and very unsportsmanlike, to say the least] to the player (especially if one's opponent requesting successive draw offers is in a clearly lost position) receiving these draw offers, but there does not appear to be any kind of penalty whatsoever [here, on chess.com] to the opponent making such repeated offers.
If an indication of 'offer draw' were present in the 'moves box' beside the corresponding move - and if chess.com implemented some kind of [say, computer-generated] TD within these tourneys [penalizing players who abuse draw offers], as well - I believe most players would think twice about when exactly they should offer a draw within these tourneys.