In the U.S., the average distance from a hospital is 10 miles (in a rural area). Assuming 55 mph speed limits, that means most people are 11 minutes from a hospital. Realistically, “speeding” in this scenario probably means something like 80 mph, so you cut your travel time to 7.5 minutes.
In other words, you just significantly increased your chances of killing your about to be born kid, your wife, yourself, and innocent bystanders just to potentially arrive at a hospital 210 seconds sooner.
Edit: the rushing someone to an ER scenario is possibly more ridiculous, since you can’t teleport yourself, and if the 3.5 minutes in the above scenario would make a difference, then driving someone to the ER is a significantly worse option than starting first aid while waiting for EMTs to arrive.