Not for stylistic reasons, but rather to express a certain thought. Something like "Here comes the end to cold weather". Just stating "End of the cold weather" wouldn't be the same. You may use it the same with people "Тебе конец" would be something like "You are done for" (correct me if I got it wrong). "Конец тебя" looks weird, even ungrammatical, and "твой конец" with current usage will remind of one's rod.
As for sequence of tenses, you may use the verb in a subordinate clause in Past, "Вчера я слушал, как канарейки пели". It is just you don't have to.