Would you rather have a world when the pay gap is lessened by making men make less money, or by making women make more money? Because this is the former, and it's not good for anyone except for Reddit's bottom line.
In the long run, it may not even be good for Reddit. The best job candidates (both male and female) will probably receive several competing job offers, and if the other companies are willing to negotiate salary while Reddit isn't, Reddit could end up losing all the best candidates to their competitors.
If they are eliminating negotiation, them either their offers need to be better than before or they'll lose talent. I suspect that the result of this will be people with less negotiating skill making more money in jobs where the skill is irrelevant to job duties and people with more negotiating skill making less than now in the same jobs at reddit. It won't be one side, and it won't particularly be about gender except to the extent that gender happens to correspond with negotiating skill and/or desire to have negotiation be part of the hiring process (the later more affecting who decides to apply to reddit in the first place.)