This metric already exists in public health, in the forms of YLL (years life lost) and DALY (disability adjusted life years [lost]). In the case of something like COVID, YLL will simply integrate expected life span minus age at death across the population, while DALY will take into account the effects of lasting disability, for example counting each year of life as only 0.8 "disability adjusted life years" for someone who suffers chronic long COVID.
Because of the difficulty of applying objective disability effect proportions, however, YLL is a much easier metric to use and there's a lot more estimates available for it as well. I found an article estimating pandemic YLL in the U.S. over 2020 to be 7,362,555 (massive 95% PI though) [1]. Interestingly, they attribute only about three quarters of these to COVID itself and about one quarter to indirect effects of the pandemic, such as lockdown. Comparing against YLL values for leading causes of death from 2016 [2], the impact of COVID in 2020 was slightly less than that of ischemic heart disease (9,445,400 YLL) but comparable to the next four causes of death (lung cancer, RTAs, pulmonary disease, colo/rectal cancer) combined.
[1] https://doi.org/10.1371/journal.pone.0256835
[2] https://doi.org/10.1001/jama.2018.0158, Table 1