Is it permissible to designate specific surahs to be recited in the Asr prayer, or the Witr prayer, or the emphasized Sunnah prayers, such as designating Surat Al-Asr and Al-Ikhlas for Asr, and is this considered an innovation (bid'ah)?

The first thing for a Muslim is to seek the guidance of the Prophet (peace be upon him) in recitation during prayer, and not to dedicate a specific prayer to a specific recitation unless it has been authentically reported from him (peace be upon him). Examples include dedicating Witr prayer to Surahs Al-A'la, Al-Kafirun, and Al-Ikhlas; Friday prayer to Surahs Al-A'la and Al-Ghashiyah, or Al-Jumu'ah and Al-Munafiqun; Fajr prayer on Friday to As-Sajdah and Hal Ata; and the two rak'ahs of Fajr (Sunnah), the two rak'ahs after Maghrib (Sunnah), and the two rak'ahs of circumambulation (Tawaf) to Al-Kafirun and Al-Ikhlas. As for other than these, it is not appropriate to dedicate them to a specific recitation. If the worshipper does so without believing in a special virtue for those surahs, it is not considered an innovation (bid'ah), because the general rule is the permissibility of reciting whatever one wishes from the Qur'an. However, if one believes that a particular surah has a special virtue (when it has not been reported), then that is forbidden by Islamic law. It is preferable to vary the recitation and not constantly stick to certain surahs, so that one does not believe they are obligatory.