Does viral DNA remain incorporated into the host genome permanently?

> Viruses incorporate their genetic material into the host genome.

No they don't. They just trick the host's cells into producing viruses.  If the police has your DNA-profile and then you get some virus-infection, DNA-traces you leave behind afterwards will still be recognised.

Yes it does. Of course sometimes the insertion will destroy the cell because the cell is tricked into making duplicate copies of the virus, and these new viruses then burst out of the cell, killing it.  Once the cell is killed, the virus DNA or RNA will not be passed on to future generations of the host. The CoronaVirus is one of those that kills cells. Therefore their DNA will not be incorporated into the host's genome.  However, some viral insertion events do not kill cells. The virus DNA then becomes part of the genome of the host. In fact, some scientists now use these inserted fragments of DNA to help them figure out evolutionary relationships. For example, 2 different species of animals that have the same inserted fragment are very likely to be close relatives, since it is more likely that they inherited the insertion from their recent common ancestor than if the exact same insertion event happened twice, independently in both species. Another species without the insertion will be less closely related. Using this method, scientists determined that the closest living relative of whales is the hippo, and that falcons are not close relatives of hawks and eagles, but they are in fact most closely related to parrots.

Only certain viruses (HIV, for example) incorporate genetic material into the genome of the host. The vast majority of viruses simply infect the cell, reproduce and (usually) kill the cell. Even viruses like Herpes simplex which establish permanent latent infections do not usually integrate their genetic material into the host chromosome.

For those rare viruses that do integrate, they are permanently integrated into the genome of the cells that were infected.

I believe viral genetic material actually attaches to the cell's DNA, so there's no way the cell would excrete it. The only way to remove it is the destruction of the cell by WBCs