A properly designed engine shouldn't have the crank throws getting anywhere close dipping in to the oil level if it's not overfilled per dipstick "full" mark. Engines also have a windage tray in the oil pan, and if properly designed it will help to keep the air "hurricane" caused by the crankshaft and pistons from disturbing the oil in the sump.
I record a few car shows on TV and saw one a month or two ago about more HP with less oil ... I think the show was Engine Masters but not sure.
iirc, they were talking about deeper pans or specially designed pans (windage, etc.) to reduce foaming, etc. and they had some dyno tests with less oil in the crank that showed a little more HP at much higher RPMs. This test was also on one specific engine so who knows.
in general, the hp gains were at VERY high RPMs not applicable to average drivers. Also the HP gains were not that significant. They didn't discuss any potential damage that low oil could cause.
Maybe if you are a race car driver it can help but those guys have specially designed engines anyway.
They also had advertisements about certain oil pans ... In general, I found the show interesting and informative but I put it under "infomercial" category and not applicable to average driver.