One problem with holding elections for local offices at the same time as national elections is that the local elections often end up overshadowed by the national elections. The more races on the ballot, the less chance a voter has to do research and make an informed decision about each race. Often people will just default to voting for their party or the incumbent. Holding local elections at a different time than national elections will allow voters to dedicate attention to local races specifically, and make it more likely that local officials will face electoral accountability for their decisions.
But separating local and national elections also has many obvious drawbacks. For one thing, elections cost money. For another, voting is not always easy for everyone. People who have a hard time going to the polls once will have an even harder time going to the polls twice, potentially harming marginalized groups. Furthermore, the voters who currently vote ‘blindly’ (such as just voting based on party affiliation or incumbency status) in local elections may just not show up to the local election at all. (Although I suppose one could argue that this is a good thing if such voters are padding the incumbency advantage to the extent that local officials can get away with anything.)