Can I use 4x4 posts as the primary support for a deck?
Around here, 4x4s are not uncommon. This table shows that a 4x4 pine post that is 6 ft or shorter can support a load area of up to 10 ft² assuming 50 lbs/ft².

Don't trust me or a random table on the internet; make our own calculations from tables in the building code or other trusted sources and consider having them checked by an engineer.