Can e-bikes speed up my commute? Which class?
Of course an ebike will be less effort and leave you less sweaty. And of course the faster the bike, the shorter the commute.

Class I: The key thing about this is that it's pedal assist only. The motor will only turn on while you're pedalling -- and it'll cut off at 20 mph -- so going faster than that will require you to pedal. Going downhill with a backwind and pedaling like a demon, you could feasibly go 40mph or faster.

Class II: These bikes have a throttle (combined usually with a pedal sensor) so the motor can turn on without pedaling. So you can go from 0 to 19.9mph without pedaling. At 20mph, regardless of whether you're using the throttle or pedal-assist, the motor will cut out and you'll have to pedal to go any faster or to maintain speed -- note that these bikes are usually heavy so even pedaling you're more than likely to quickly lose speed back down to 19.9mph unless you are pretty buff or you're going downhill. Technically, Class II  are limited to 20mph for electric assist but it's often possible to bypass that control with a firmware upgrade or setting in the control panel.  


  Speed Limiters: On most Class I and II bikes, the speed limiter is a hard cutoff. The motor can give you 100% power up until 19.9 mph and then when you hit 20.0 mph, the motor gives you 0% power and you have to pedal to maintain speed. The bike usually quickly loses speed (as pedaling a heavy bike at 20.0 mph is non-trivial) and the motor kicks back in at 19.9 mph. This can cause some jerkiness around the speed-limiter zone especially if you were using pedal-assist because the bike suddenly gets very heavy at 20 mph (it's not as noticeable with a throttle, where it just feels like the motor is cutting in and out).  More expensive bikes will more smoothly ramp the power down: 100% power at 19.0 mph; 80% power at 19.2 mph; 60% at 19.4; etc. etc. and then smoothly ramp the power back up while  you're accelerating. 


Class III: These bikes have a throttle (combined usually with a pedal sensor) so the motor can turn on without pedaling. These are limited to 28mph for electric assist but it's often possible to bypass that control with a firmware upgrade or setting in the control panel.  For example, some are sold with an "off-road only" switch. 

All of these are limited to 750 watts of electric assist power as well. For more info: https://electricbikereview.com/guides/electric-bike-classes/