You are incorrect. Posts will rot must faster and will not be stable in just clay. Posts rot in concrete because they are installed incorrectly. The concrete is usually below or at grade and the water will pool on top of the concrete surrounding the wood. Thus, causing rot.
Most building codes require 6' feet height limits. Some less. There is no standard. Check your local code and CCR or build back the same height. Use kiln dried pressure treated posts. NOT from lowes or depot!!! 4x4 will work, but I always use 6x6 at gates if using wood. Dig a hole at minimum two feet. Closer to three is better. Fill with concrete to grade and have a little xtra concrete left over. Once it starts to set a little bit, shape some of the remaining concrete a little up the post (above grade) and away from the post at an angle like this /lllllll\. The water will then run away from the post base and wont be able to collect against the wood. Use a trowl or a small piece of wet wood to smooth it and make it look nice. It's also advisable to paint or use another product to protect the wood. If not paint, I like Waterlox Marine or OSMO products. Spar varnishes are the next best with multiple (a Lot!) of coats
The posts will be there long after you are not