LA’s tap water is actually pretty good at the source level if you don’t mind a bit of arsenic. By the time it reaches your faucet, it may be pretty cruddy from aging, corroded pipes between you and the DWP source, or it may be fine.
LA’s water passes all federal & state standards, but that’s not the same as “completely pure” and not necessarily the same as “safe to drink” (especially with regard to arsenic).
(Arsenic is a natural contaminant, and is very expensive to remove - basically, you’d have to turn the whole water supply into Dasani to get rid of it. For most tap water uses - washing, gardening, flushing toilets, etc. - it makes no difference. But anyone with a developing neural system - young children, and pregnant and nursing mothers – should not rely on it as a primary drinking-water source.)
Filter pitchers or simple inline cartridges filters will usually deal with taste/turbidity problems caused by aging plumbing, but they do nothing at all about arsenic or most other health-concern contaminants.