How do they work together when there are fundamental disagreements with the path forward? Labour won’t be able to criticise how the Tories have run if they have a foot in their plan? The same would be said of the reverse. Also, the Tories would say it all went wrong because of Labour sabotage. The incentives aren’t there and they never will be for something like this.
The only time it’s possible is during an external threat, like in WWII.