HolySox There is absolutely no guarantee that the virus will burn out. Viruses don't work like that. Just think about influenza or the common cold, which have never "burnt out". Diseases like measles have never burnt out either, although vaccinations usually keep it under control.
Theoretically, coronavirus could mutate, so that another variant becomes more transmissible but less dangerous. The new variant could, in theory, replace what we have now. On the other hand, there could be more dangerous mutations. We just don't know.
The only serious solution is a vaccine, which would need to be adjusted regularly to deal with new variants - just as the flu vaccine is. That's why it's advantageous to keep transmission low. The more the virus is transmitted, the more opportunities there are for mutation. Therefore, it makes absolute sense to continue with mitigation measures which cause the least inconvenience.
It is entirely possible that there will never be herd immunity.