it would be much simpler to further heat the steam at the ambient pressure of the autoclave room
You cannot do that, physically. If you put water in a closed (water-vapor-tight) container, then heat it, the vapor "wants" to expand with growing temperature. But as it cannot expand your metal container (autoclave), the pressure goes up instead. It happens automatically, that's how molecules function in a gas (don't ask me to remember the name of that law please).
You could, I guess, try constructing an elastic autoclave where the pressure stays the same and the volume changes. But that would be mechanically challenging - what material are you going to use that is elastic, won't tire with time, won't deform on you during use, won't burn at the heat source, will conduct warmth well, etc.? Also, you will lose your convenient way of ensuring that you are at a target temperature. Since a certain pressure always equals a certain temperature (at constant volume), you can construct a weighted valve to keep a constant pressure in your autoclave - this is cheap, easily doable with 19th century tech, and more accurate and failsafe than creating a cybernetic control loop with a measuring device such as a thermometer or a manometer.
I don't know if there are also biological reasons to prefer it with with a higher pressure - the number of bacterial species which can withstand high temperature is higher or equal to the number of species which can withstand high temperature combined with high pressure - but I doubt that this was a driving factor in the design and adoption of autoclaves.
The standard autoclave is easy to invent, does its job, does it well, and is cheap and unfussy (when compared to a hypothetical room-pressure-wet-autoclave). The pressure is more of a side effect nobody sees the need to remove - on this site, I'm tempted to call it a spandrel.