"First wash... Then dry... What if it was done right away?"

Here are the main advantages of a washer-dryer (2-in-1) compared to separate washers and dryers:
Space saving
The biggest advantage. Ideal for small apartments where there is no space for two separate appliances.
Convenience
All in one: No need to move laundry from the washer to the dryer.
Automatic cycles: Some models start the dryer immediately after washing.
Aesthetics and ease of connection
One appliance - fewer hoses, less electricity, easier connection.
Looks better in the interior.
Price (sometimes)
One appliance is often cheaper than buying two separate good quality machines.
Less maintenance/repairs
One unit - less chance of breakdown in general (although the risk that in case of breakdown everything is lost at once).
Energy efficiency (in newer models)
Some modern washer-dryers have a heat pump, which saves a lot of energy.
Although washer-dryers have their drawbacks (such as less drying efficiency or smaller drying loads), if space is limited or simplicity is required, this is a very worthy option.