  For $n\ge 4$, we show that there are infinitely many formally contact
isotopic embeddings of $(ST^*S^{n-1},\xi_{\mathrm{std}})$ to
$(S^{2n-1},\xi_{\mathrm{std}})$ that are not contact isotopic. This resolves a
conjecture of Casals and Etnyre except for the $n=3$ case. The argument does
not appeal to the surgery formula of critical handle attachment for Floer
theory/SFT.
