You are 100% correct. Few people actually support this on either side.
So therefore it would be VERY easy for the Senate to legislate a fix very quickly and solve it once and for all.
Sadly, on both sides, I think the politicians are more interested in using he current situation as a weapon to bash the other side than to actually fix it.
That is the sad story. Both sides basically want the situation to continue since they feel they can gain some political benefit out of it.
Take the both sides language out.
Trump and his admin is the only reason this is happening. Period. There is no both sides.