Counterintuitively, this is far more expensive than launching it into said black hole, or just out of the Solar System all together.
The earth is orbiting the sun at 30 kilometers per second. So if we launched something into space, since it started on earth, it would have that speed (similar-ish to throwing a ball from a moving car). So that object would now also be orbiting the sun at 30 km/s. We would need to slow it down that much in order to "fall" into the sun.
Once something was in earth orbit, it would only take about 12 km/s of delta v (change in velocity) to escape the solar system.
More info and math here: https://space.stackexchange.com/questions/3612/calculating-s...
Sad note that also limits your launch window to once every 113 years as I recall from the last time I did the math :-(.
From a technical perspective you push into an elliptical orbit that intersects Venus, you do a slight aerobreak (skim the surface of the atmosphere) to dogleg toward a Mercury intercept, and then as you pass Mercury it tightens your ellipse still further and you head out, and come back and fly through the outer corona of the Sun (which is its hottest point). At which point you're in a degenerate orbit that will go out and come back through the Sun's corona until you've been completely consumed/burned up.
This is the first order approximation reason.
As a counter example, someone mentioned nearly leaving and then cheaply coming back directly into the sun.
While spinning it’s hard to get to the center. Once it stops, it’s easy.
The earth is spinning around the sun. To get to the sun, you need to slow down.
