Unfortunately, there isn’t a clear definition of place=suburb in the U.S., because we use that word so differently in official and colloquial speech. Based on my working knowledge of OSMian English, a suburb is part of a town or city. I tend to use this tag for a village that has gotten absorbed into a larger city through annexation but kept its original identity, but since place=town/city aren’t strictly tied to incorporated places, I suppose it’s OK to tag a place=suburb if it “feels like” a city neighborhood and most people wouldn’t think of it as an independent place. Assessing that feel is too meta and hypothetical for me, so I stick to hamlet/village/town outside the city limits and it seems to stick.
Something to keep in mind about CDPs is that they’re statistical areas first and foremost. Since 2010, there’s been a best effort to align them to colloquial notions of unincorporated places, but demographic realities sometimes outweigh that goal.
CDPs also have a stronger tie to administrative boundaries than place=* tagging. For example, the CDP of Alum Rock, California, consists of all the portions of Alum Rock that stayed unincorporated after the City of San José annexed a third of the community, including the business district at its core. Therefore, the C-shaped CDP’s label member is located outside the CDP and inside the city limits, doubling as a representation of the city’s Alum Rock neighborhood.
A similar thing happened to the village of Covedale, Ohio, back in 1930. Parts of the village that Cincinnati didn’t annex reverted to unincorporated Green and Delhi townships. Later, the Census Bureau reused the name Covedale for a CDP in southern Green Township, excluding the Delhi Township portions but including much, much more than the original Green Township portions. Only the portions of the CDP closer to the GNIS place node strongly identify as Covedale.
Conceptually, I favor tagging the central city of a metropolitan area as a place=city. A metropolitan area usually has a ring of suburbia[1] around it, or at least the potential for an urban–suburban hierarchy. In practice, this means that I’d tag the largest principal city of an MSA as a place=city, and sometimes the other principal cities in a polycentric MSA. But I don’t favor automatically promoting other principal cities of an MSA. The criteria for a principal city would nicely fit place=city, except that the “additional places” clause makes it nothing more than a population threshold of 10,000 or more, defeating the purpose of considering statistical areas in this determination.
The Los Angeles–Long Beach–Anaheim MSA has 19 principal cities, but of them, I’d only consider the three cities in the MSA’s name to be good candidates for place=city, or at most the six cities named in the Anaheim–Santa Ana–Irvine and Los Angeles–Long Beach–Glendale metropolitan divisions. Otherwise, if we promote every principal city to a city, then we’re back at square one with lots of city nodes cluttering up big metro areas.
The other principal cities of a CSA would be even worse candidates for place=city in most cases. These cities are named because they are the largest place in either an MSA or a μSA, regardless of absolute population. A principal city can be as small as Atchison, Kansas, with a population less than 11,000. Atchison is the principal city of the eponymous μSA, which is part of the Kansas City–Overland Park–Kansas City CSA, being joined to the hip of the Kansas City MSA for economic reasons. I disagree with how lots of cities in the Kansas City area like Gladstone, Missouri have been tagged as place=city, as if they aren’t suburbs[1:1] of Kansas City. But it’s even clearer that Atchison shouldn’t even be on the same footing as those cities. Plenty of μSA principal cities are fine as place=town; they become rather less prominent, not more prominent, when the μSA is part of a CSA.