It's not just a question of total power - smartphones have limited space and thermal budget for internal power conversion compared to laptops, which means that the fastest charging option often moves some of the work of converting to the correct voltage to the charger. (Also, I don't think 240W USB PD has really been adopted by anyone currently, and that's a spicy amount of current given the general quality of USB C cables.)
It depends. USB-C supports PPS, which allows the charged device to request a specific voltage, so conversion is no longer needed.
The specification does mandate that the device must be able to fall back to a static voltage if the charger does not support PPS, though. But in practice a device could totally require PPS for fast charging, and only do trickle charging with a non-PPS charger.
> But in practice a device could totally require PPS for fast charging, and only do trickle charging with a non-PPS charger.
Not sure we have the same terms. Trickle charging is 0.02-0.05C charging to see if the charger can get the battery safely from being overdischarged to say 3V where it can start normal CC charging phase.
That would probably piss off a lot of users and the EU if not even normal charging was supported by a device connected to any USB charger, because that's back to requiring a specific charger for each device, where not even basic things that all users expect work anymore with all conforming chargers.