it probably won't be a good idea to impute a variable with ~80% missing data is not entirely accurate as it depends on the nature of the missingness and the information in the other variables that are non-missing.
The first is the nature of missingness. Are the data missing at random, observed at random, or missing completely at random? There are many useful resources on the definitions of MAR, OAR, and MCAR.
The second is how much information you happen to have about the missings. If there are close correlates of the variable with missing values and the relationship between the correlates and the variable with missing data is independent of the missingness, then imputing it allows you to retain the information you know and generate reasonable imputations of the rest so that the information that you do have observed can be used. If the data are panel/longitudinal, the two-dimensions can often be usefully deployed as informative for the missing values.
Personally, I am more persuaded by the one should always impute data unless you have good reasons not to that relate to the above conditions. Omitting the variable is throwing away information which I am not convinced one should ever do without good reasons.