nobody
i take no offense but a heter is a heter. it is a very, very important component of Halachah. it is not a bad thing. the greatest Poskim often would spend hours of their precious time searching to find a heter for someone in need.
even for availus, not everyone is holding at such a high madrayga as you. in answer to your question, many times during availus a family simcha, such as a daughters Chasunah might arise, and one might look for heterim, even during availus, to be there for ones precious child. there could be many more reasons for looking for heterim during availus.
i do agree in general though with your lofty understanding of what availus is