Is it permissible to go to the mosque late intentionally to catch the last rak'ah and complete the prayer alone due to the fast pace of prayer in mosques?

One should not intentionally and consistently delay prayer. If the swiftness of prayer in mosques does not affect the validity of the prayer and the attainment of tranquility, then there is no harm in it. The Prophet (peace and blessings of Allah be upon him) said: "Come forward and follow me, and let those behind you follow you. For people will continue to delay themselves until Allah delays them." However, if the swiftness affects the validity of the prayer by losing tranquility, then it is not permissible to pray behind such an Imam.