If the Sun became a black hole...

If the Sun somehow managed to become a black hole, then its gravitational force would still be the same and the Earth would continue to orbit it as if nothing happened. However, I saw a video by TheBadAstronomer who said that because the black hole would be tiny, the Earth would be able to get closer to the Sun so eventually the gravitational force/acceleration would get stronger and stronger, and the Earth would be engulfed by the Sun.

But surely if the black hole were tiny, then the distance between the Earth and the Sun would be much higher, so the Earth would experience a weaker gravitational force from the Sun? Also, why would the Earth start to get closer to the Sun in the first place?

If the sun became a black hole, it would still have the same mass as when it was a star.

The earth is already (very) slowly travelling towards the sun I believe, but I'm not sure about this.

If the Sun somehow managed to become a black hole, then its gravitational force would still be the same and the Earth would continue to orbit it as if nothing happened. However, I saw a video by TheBadAstronomer who said that because the black hole would be tiny, the Earth would be able to get closer to the Sun so eventually the gravitational force/acceleration would get stronger and stronger, and the Earth would be engulfed by the Sun.

But surely if the black hole were tiny, then the distance between the Earth and the Sun would be much higher, so the Earth would experience a weaker gravitational force from the Sun? Also, why would the Earth start to get closer to the Sun in the first place?

I should probably mention, I'd be more interested in the planet's motion/physics in this scenario rather than the loss of life/heat/light etc :P

The distance between the centre of the Earth and the centre of the Sun/Black Hole would be the same however big or small the Sun was. You must be thinking of the distance to the surface. The gravitational force depends on the distance between the centres of mass.
He didn't say the Earth was getting closer to the Sun. He said that if the Sun (its diameter) was smaller you could get closer to the centre of mass.

So if the Sun were replaced by a black hole, then the Earth would just continue to orbit it and not get any closer? But if something did managed to strike the black hole (e.g. several million asteroids), then would that cause the Earth to become pulled into the black hole due to the stronger gravitational force due to its higher mass (if that's true, then I assume that would apply to the Sun in its present state as well)?

So if the Sun were replaced by a black hole, then the Earth would just continue to orbit it and not get any closer? But if something did managed to strike the black hole (e.g. several million asteroids), then would that cause the Earth to become pulled into the black hole due to the stronger gravitational force due to its higher mass (if that's true, then I assume that would apply to the Sun in its present state as well)?