Does the prayer of one who deliberately fails to catch the Fatihah with the Imam in Tarawih prayer become invalid? And is the permissibility for a latecomer not to catch the Fatihah a concession for those who did not do so intentionally?

The prayer is not invalidated by what was mentioned. A man is considered to have caught the rak'ah with the Imam as long as he caught the ruku', even if he was late in beginning the prayer with him and missed the recitation. It is stated in Tuhfat al-Muhtaj: "If the ma'mum (follower) catches the Imam while he is bowing, he has caught the rak'ah – meaning what he missed of its standing and recitation – even if he was negligent by delaying his taharrum (beginning of prayer) for no excuse until he bowed, due to the authentic hadith (definition) concerning this."