When my Paladin had barding inspiration and landed a hit, he could choose between inspiration damage bonus or using smite but not both. Shouldn't he be able to do so?
Yes. Using Bardic inspiration costs no action so can be done alongside anything else.
But TBH I'm just happy that it sounds like there's an option not to automatically spend inspiration. That was some where around a reduction to 1/4 of the chance for it change a result under generous assumptions. But it's such an easy feature to automate entirely somewhat sensibly, and really just requires a degree of failure threshold to be as customisable as you need for almost every situation.
