>there's no guarantee that it leads to accurate score function? But aren't the score matching algorithms (denoising, projection) supposed to be able to solve the objective function involving grad_x log p(x)?

Oh no it's not. All it's doing is to minimize the mean-squares error against the score function. Minimizing this objective does not mean sampling using this score function will be a good idea; which it isn't. This is exactly why score modelling has to rely on adding noise. And by doing this, they converged to DDPM.