I would check the expected damage compared to a regular attack. If this is less than the normal attack (taking into account the relevant vulnerabilities/resistances/immunities), then I would not care because I would consider it flavor (i.e. roleplaying).
Likewise, if a player would be smart enough to discuss this while in a town with a smithy, and they might as well buy a warhammer or other bludgeoning-dealing-weapon, but would ask me to flavor it such that the shield would act as that weapon, then I'd allow it... on the condition that the shield does not give an AC bonus in the turn that it's used on the attack.
But if a powergamer would want to maximize damage right there on the spot, with no preparations, then I would likely explain that it is an improvised weapon and push back. I hate powergamers that are playing this game exclusively to be the most powerful player. But on that matter, I am probably not your average DM.