I am not sure of the probably very interesting history on the draw offer in chess.
Not that I really like the idea. I personally as an active chess player most often endeavored to never offer a draw, and by default considered to reject any draw offer, no matter of the consequences of if losing, or even drawing anyway, or winning. As an active chess trainer, I generally always promote to all my students the same I strongly believe to be high sportive standards.
I am quite sure that if a draw offer is allowed (as it usually still is), a resignation offer (a regular in friendly chess games) should be considered to be allowed, too. On disturbing, both types of offers can potentially disturb the opponent. The exact wording could be “I offer you to resign.”, with a compulsory mark of the offer on the scoresheet (after the move played) with a respective winning result for the side proposing (1-0, 0-1).
Benefits of a resignation offer:
Often a player when having a completely lost position continues to play by inertia, and especially if in time trouble while not yet reached the first time control, if any. Sometimes usually the weaker player is not very sure the position is hopelessly lost. In this case the stronger player having a completely won position can basically hint to the weaker player (in a very straight-forward way, as opposed to making hand or face gestures with the same purpose) that it may be the time to resign the game and move on. Inclusive of simultaneous chess exhibitions.
With the progression towards all chess players having a rating (standard, rapid, blitz), an improvement over current could be allowing draw offers by the higher rated player only, which would additionally contribute towards raising rating/ranking awareness.