Wood rail on concrete steps
For 4x4 posts mounted on their butt end to a concrete surface it seems like a robust solution. One concern is that if you ever have any rotting and some of the wood ever needs replacing it will be rather difficult to remove these posts. If it is a solution that you would expect to get 5 to 10 years of average service life out of then the solution will work nicely.

One nice aspect of the described solution is that it lets the post sit right on the concrete without any visible fasteners. Any other type of post butt fastener is going to show some type of metal brackets that could detract from the aesthetic.