Safe in the sense of frequent. Not safe in the sense of profitable. Those are different claims and the word "safe" quietly does both jobs.
The favourite wins 35% of races. Nothing else you can pick without study comes close: a horse chosen at random wins around one time in eight. If what you want is to see your selection come first reasonably often, backing favourites delivers that.
Across 29,687 races, backing every favourite at level stakes has returned -8.98%, which is about 9.0p lost in the pound.
We have a deep page that works through this in detail, with the year-by-year figures and the breakdowns by code and field size: Does Backing the Favourite Make Money? This piece is the short answer, in the words people actually use when they ask.

