Why not.

However, programs mostly rely on other programs ( your code -> your interpreter/compiler -> libraries -> OS -> firmware) and all of that relies on hardware.

Any of these can have bugs, there are hardware failures and poorly implemented or just worn down hardware.

It is almost entirely impractical for the vast majority of applications being written today, and the costs of developing perfectly bug-free software would outweigh the benefits.

Just because something is possible does not mean it it probable.
The more complex the software the greater the likelihood of a bug.

so long as no new features are added or no new complexity is added to the software - given sufficient iterations of testing and bug-removal it may be possible to become bug-free?

until bug getting found (cought?) a program is considered bug-free

Being able to recognize if an arbitrary program is bug-free would violate halting problem.
Therefore the statement can not be proved for arbitrary programs, which I assume, is the interesting case of the premise.