Wolf, name ONE SPECIFIC ROV anywhere even debatably near Rav Chaim’s stature who disagrees with the important nature of a hat/jacket (putting aside the precedence question.)
Ah, but what you want to “put aside” is just the case we’re discussing. We’re discussing a case where a person has a choice — daven alone or with a minyan without a hat/jacket. R. Chaim is entitled to pasken one way, but, WADR, that does not mean that his p’sak is halacha l’ma’aseh for everyone.
If you want to argue about whether it’s better (in general) to wear a hat/jacket or not to, that’s a separate argument.
The Wolf