stupid proposal, i like it the way it is.
The change would be subtle and wouldn’t necessarily require that both teams get possession. Any touchdown would still result in a sudden-death result.
However, if the team that got the first possession of overtime scored only a field goal, the other team would get a possession. If the second team scored a touchdown, it would win. If it scored a field goal, the game would continue, whereupon it would revert to simple sudden death.
Also, if the first team to get the ball didn’t score but the second team did, the game would be over immediately.