It is well-known that the Gromov-Witten invariants and their Floer-theoretic counterpart of symplectic manifolds have rich algebraic structures. However, sometimes it's quite useful even by considering the moduli spaces of solutions of $J$-holomorphic or Floer equations. For example:
Gromov's original characterization of homotopy types of the symplectomorphism groups of $\mathbb{CP}^2$ and $\mathbb{P}^1 \times \mathbb{P}^1$, by considering foliations by $J$-holomorphic curves;
McDuff' construction of cohomologous but non-symplectomorphic symplectic structures, by looking at bordism classes of certain moduli spaces;
Hofer's proof of the degenerate Arnol'd conjecture for symplectically aspherical manifolds;
McDuff's proof of the uniqueness of the symplectic filling of standard contact $S^{2n-1}$ up to diffeomorphism, and in the similar spirit, Wendl's result on fillings of planar open book decompositions of $3$-manifolds;
Abouzaid's construction of the bounding parallelizable manifold of exact Lagrangian spheres in $T^* S^{4k+1}$.
Question: modulo direct generalizations and improvements of the above results, and Floer-homotopical considerations, what are some other geometric applications of the geometry of the moduli spaces of $J$-holomorphic curves (or solutions to Floer equations)?