There is not much space left for improvement.

But if I am doing this, I probably will not use $., instead just count lines myself, which is not a big deal.

Personally I would think (100% personal), using $. reduces maintainability. If one day, you (or someone) decide to modify your code for whatever reason, and in your while loop a second file is involved, your program can be easily broken, as there is only one $. across all files, and the value is only true for the last file handler accessed.