Why is a 3 degree descent angle used?
Basically, it's a combination of historical significance, passenger comfort, and ease of mental calculation.

Historically, before aircraft were pressurized a rapid descent would be uncomfortable for passengers. At the speeds typically flown, a 300ft/min descent was deemed to be comfortable enough for the typical passenger.


  Many aircraft had a cruising speed between 100–120 miles per hour (160–190 km/h). Three miles would be traveled in about 1.5–1.8 minutes, resulting in a rate of descent of about 550–660 feet per minute. That was about as fast as passengers could comfortably adapt to the changing pressure on their eardrums. However, many pilots used a 300-feet-per-minute descent rate because doing so is almost unnoticed by passengers. A pilot cruising at 10,500 feet would calculate that in order to be at 1,000 feet at his destination, he would have to descend 9,500 feet. Dividing 9,500 feet by 300 feet per minute, that descent would require about 32 minutes. If his ground speed was 120 miles per hour (190 km/h), he would begin his descent about 64 miles (103 km) from his destination (traffic permitting).


As you can see, there is a reasonably simple mental calculation that can be done there. This is commonly referred to as the rule of three which is in part quoted above.

That covers descent from cruising altitude, however you are right that flight in IFR will depend on procedures, and scenario. An example is London City Airport which uses a much steeper descent profile of 5.5 degrees on approach to land.