If we interpret "the power" in this case to refer to bargaining power, then oddly enough, the Internet has been the worst thing for mail-order brides (and their less-remote equivalents, "sugar babies.")

Look at a "regular" dating site: there are far more active male users than female, the men send almost all the messages, and the women reply to nearly none of them.

Now look at one of these mail-order bride "dating" sites, or, equivalently, a "sugar-baby" site like SeekingArrangement—where, in either case, the men come pre-qualified as having money and being willing to give that money to the women: now, on these sites, there are far more active female users than male, the women send almost all the messages, and the men reply to nearly none of them.

When you take non-wealthy men out of the dating pool, suddenly there are few enough men left that supply-and-demand forces women to compete over men. Which puts them in a much weaker negotiating position than they would be otherwise.