In my use, it would depend on the (supposed) reason for the seedlings failure. Many people get failures in seed sowing , often in my experience, due to not providing a correct temperature to germinate, and/or ,over watering. Multipurpose composts can hold lots of water, yet appear dry on the surface. Rather than just add more, I sometimes ‘weigh’ the tray to see how heavy it feels.
Once you have given up on a tray, then unless the suspected failure can be attributed to either of the above, one needs to decide if the seedlings did appear, and then fail, perhaps due to fungal(damping of), or a slug/woodlouse attack.
Hopefully new compost from commercial sources will be sterile, most folk are not able or willing to re-sterilise, so personally would elect not to re-seed in that tray, but have no qualms in using the ‘rejected’ compost for potting on more established plants.
Garden composts do not generally cause problems for most uses, and contain plant material from previous use.All used composts can be added into the heap here.
Charles may disagree..