Yes, it's absolutely good idea to have the upgraded insurance in place at or before completion, not afterward. Condition the SPA on it — either as a closing condition or a seller obligation. Execution is key and you may implement It in the SPA: Couple of practical options that I can suggest:
Option A: Closing Condition"Completion of this agreement is conditional upon the Company obtaining an insurance policy covering the full replacement value (or business interruption value) of its inventory, on terms acceptable to the Buyer."This gives you leverage to walk away if it's not in place.
Option B: Seller Covenant / Undertaking like £"The Seller undertakes to procure that, prior to Completion, the Company shall upgrade its inventory insurance to cover replacement cost and extended business interruption, and shall provide evidence of such coverage to the Buyer." Or similar one Option C # Indemnity or Escrow If for unpredictable reasons the seller pushes back on doing it pre-close, then your only moot is to imposeAn indemnity clause for inventory loss between signing and closing.A purchase price escrow to cover potential uninsured losses during that window.

You may want to explore a stock thru-put. It's a more expansive coverage for inventory. Deductibles are usually lower, coverage usually extends to also cover the items while in transit, and the carriers can manuscript the wording- so there's more flexibility to tailor the coverage to the client. Sometimes it can be a better price as well.