Free discovery sounds client-friendly. In practice, it pushes the cost of scoping onto the vendor, which means the vendor has to recoup it somewhere — usually by inflating the build estimate or by rushing the discovery itself.
We charge $1,500 for a two-week paid discovery. The deliverable is yours to keep whether or not we end up building together. Three things consistently happen when both sides have skin in the game: the client takes the kickoff meeting more seriously, the engineers ask sharper questions, and the eventual estimate is roughly half the variance of the free-discovery estimates we used to do.
If $1,500 is too much to test the relationship, the project budget probably isn't there.