I believe their main purpose in life is to keep the exhaust temperature higher for cleaner emissions. That's the reason they began life on Subarus back in the 1970s. I'd wonder if removing them would make any difference to the O2 sensors.
Mine apparently were getting rattly for the PO because someone tack welded them together.
Shields may also protect the body paint from high temperatures> paint failure> corrosion.
There's not enough heat shield to protect the pax side CV axle inner boot on my 99 Forester. It failed w/ enormous volumes of black smoke from grease on the catalytic converter. It scared my daughter badly who thought the car was on fire.
I see. I'll probably tear them off as they are in the way while I troubleshoot and repair stuff and put them all back later. Not surprised ddavidv inherited those welds...but dang, what a pain if you need to get in there.