According to 2016 ITF Fed Cup Regulations:
33. TIE - HOW DECIDED
iv) For all Ties in the World Group and World Group II;
With respect to the second day, if the third singles decides the outcome of the Tie, the fourth singles match will not be played and the dead doubles will be played instead.
If the fourth singles match decides the outcome of the Tie the dead
doubles match will be played.
So one possible answer to your question could be simply because the rules say so.
However, we might still ask what motivated that the rules are stated this way. (Although answers to this might be, to some extent, speculative.) There might be several factors:
- For the teams it might be good that young players might gain Fed Cup experience. So they are more likely to appear in dead rubbers. (For example, I am not sure whether 18-years old Daria Kasatkina would have played her first Fed Cup match this weekend, if the match had not been already decided before the doubles. If you look at last year's Fed Cup World Group matches, you will find some players without previous Fed Cup experience in dead rubbers, such as Denisa Allertová or Vitalia Diatchenko.)
- From the viewpoint of ITF, which is the governing organization of Fed Cup, they might try to seek balance between not to put too much strain on players (who complain about long season and too many matches to play anyway) and having something to show to spectators (which definitely want to watch some tennis, even if the match is already decided). Quote from the article ITF revises Fed Cup dead rubber policy on the Fed Cup website (February 2013) supports this point:
ITF Executive Vice President Juan Margets said: “The enhancement of the dead rubber policy came in response to requests from players, captains and National Associations following its successful introduction in Davis Cup. This is part of the ITF’s continued effort to make Fed Cup more player friendly, while maintaining a good spectator experience on the Sunday."
There is also one more thing, but I never heard about a case where this rule was actually applied. (And I hope there never will be such case.) In the case that a player played in the final and has a positive doping test, even the matches which were originally dead rubbers might matter for the final result.
I will quote the Fed Cup Regulations again:
If any player following completion of the procedures, including appeal, set forth in the ITF Tennis Anti-Doping Programme is found to have committed a Doping Offence whether in a tournament and/or in out-of competition testing and/or in any round of the Competition, and/or otherwise, no disqualified match result shall be re-assessed except in the case of the Finals where such player’s wins (if any) will be reversed and all unplayed dead rubbers will be awarded to the opposing team of such player. This may result in the team which originally lost the final being declared the Champion Nation.