The Shulchan Aruch writes that every yirei shamayim should be disturbed and worried over the
fact that the Bais HaMikdash has not been rebuilt.

Regarding Tikun Chatzos – this is not a chiyuv but rather a very important thing to do, as emphasized by the mekubalim. The time for this is at Chatzos, since at this time Hashem woes over His children, that their sins caused the Bais Hamikdosh to be destroyed, and the Heichal to be
burnt, and the people to go into Galus. However if this time is difficult then one can say it at עלות השחר.
If so, why don’t we say it? The most important part of Tikun Chatzos is the woeing and crying
over the Churban Bais Hamikdosh, feeling pain from the Churban. Unfortunately we are not
holding by this level and for us to sit on the floor with ashes on our head and wearing a sack
will be meaningless. There are people that say Tikun Chatzos during the 3 weeks/ 9 days, since
during these days we have more of a feel for the Churban, which gives the Tikun Chatzos more of a meaning.