Perhaps praying privately keeps a woman focused on Allah (subhana wa ta’ala) and not on how others are viewing her prayer, minimizing the chances of her praying for show. Perhaps this is also the reason that men are rewarded more for praying Sunnat and Nawafil at home rather than in the Masjid, while for them the Fard prayer is much more highly rewarded in the Masjid.
Allah (subhana wa ta’ala) knows best how He purifies our deeds so that they are purely for Him. Any deed not done for Allah (subhana wa ta’ala) will be a cause of regret for us on the Day of Judgement for it will have no weight and no reward. Only Allah (subhana wa ta’al) will reward that Day and He will only reward whatever we did seeking His pleasure alone, while those deeds we did for other than Allah (subhana wa ta’ala) will be useless for us.
One of the names of the Day of Judgement is Yawm al-Hasara (the Day of Regret). Each person who did good deeds will regret not doing even more good deeds seeing how wonderful is the reward for them, while he who did evil deeds will regret having done them seeing how awful is the punishment for them.