Pressure Volume Cycle

if a higher compression ratio is ideal for power and uses more exhaust gasses for power what are the benefits of lower compression ratio engines.

That's a very broad question. There are multiple reasons to have higher or lower compression for a particular application. For example on some diesel applications, compression started to get lowered to help with NOx and particulate matter at part load. Generally in the OE, they will implement enough compression in an engine to promote uniform fuel burn and to not experience pre ignition from excessive compression temperature.

Although higher compression can increase overall peak cylinder pressure, compression ratio tends to have more of an influence on combustion speed and pressure and temperature of the combustion chamber at the peak of the compression / before and ignition event.

Depending on the available octane and anti knock index of the fuel you are using, you may have different requirements for compression, as a general rule, higher compression engines require higher quality, high octane fuel to prevent detonation.

Then if you delve into atkins and miller cycle engines, the static compression is higher due to different valve timing to lower dynamic compression and compression temperature, but try for a higher expansion ratio.

As Nathan said, lower compression will usually result in a lower peak combustion temperature, which can lower oxides of nitrogen in the exhaust gases. They are toxic, and you may recall the VAG "dieselgate".

The other thing, as Nathan also mentioned, is the higher compression tmeperatures reached, which required a fuel resistant to those.

Other than that, I can only think of negatives.

Lower compression ratio keeps extracting power much longer after TDC comparing to higher CR that allows to reduce high stress on pistons, rings, bearings by avoiding very high pressure peaks thus increases engine overall longevity.