There are definitely more cars going to rohtang than the permit limit.
Like you we haven't been able to god's own country or any other southern state.
Since childhood we travel with our own car and going to south or even north east is a difficult task.
Even the 14hour ride to manali was exhausting for my family and even for me.
I was giving a ten rupee note (thinking of it as a 200rs note) to the guy collecting green tax as we enter manali.
Going to south or northeast states would take atleast 3 days one side.
Next option is to go by airplane and getting a rental car but that will be too costly.
But yeah will definitely visit these places.