Man-shaped robots aka androids may have their uses, but it's quite possible that the Federation makes do without those. The principal reason for using androids would be to allow them to operate machinery interchangeably with humans - but if the idea is that humans shouldn't do work, then the machinery wouldn't need to be built to be compatible with humans in the first place. Instead of making an android use a broom, the Federation then would employ broom-shaped robots, or self-swiping sidewalks.
Wherever Data goes, he's derided rather than worshipped. Cultures that don't know how to build machine men consider him an abomination; cultures that do consider him a fancy trinket, perhaps a sick joke at Noonien Soong's expense or something. If machine men were a regular phenomenon, Data probably would suffer somewhat different treatment, being initially mistaken for one of the stupid automatons, say.
Androids may have been a phase the UFP went through in the early days: Kirk was somewhat impressed by certain alien ones (but not others) in the 2260s, while Harry Mudd made criminal use of machine men of unknown origin in the 2250s already, leaving nobody impressed. After this phase, some vaguely android robots such as the DOTs might see use, until they, too, would disappear in favor of the self-sweeping sidewalks and self-sealing stem bolts.
Or then androids persist as a civilian phenomenon, and are considered something of an embarrassment by Starfleet - either in the sense of them being the equivalent of paisley-patterned camo gear or strawberry-flavored field rations, or in the sense of them being the equivalent of battery-powered sex toys.
Timo Saloniemi