Because of air pollution being greatly reduced,this city is

Because of air pollution being greatly reduced,this city is still a good place to live___需要加in
1、不定式为不及物动词,其后应该有介词.2、但是不定式修饰time、place、way可以省略介词.比如He has no place to live.我的疑问就在于按照以上两个理由,上面那句话应该不需要加in,我想知道原因,
你说的我都知道，我困惑的就在于place,time,way这些词不是可以省略掉介词吗？就像我问题中具的例子：He has no place to stay/live。这个后面就不需要用in。为什么那句就需要用in。