DRT depends on the circumstances, but it is certainly possible with handguns same as with any other appropriate "tool". Size of animal, a visible kill zone with angle, range, stationary/walking/running, temperament, cartridge/load, the shooters experiance/confidence/ability with "that" tool so shot placement, and on and on.
I've killed a ton of game with handguns from the late 50's (mostly P&V and cook pot fodder with revolvers/22 auto pistols); everything up to big game from the mid 60's (with revolvers and specialty handguns). Were they all DRT? Because I used handguns for so many species the numbers depend which species from small diggers to elk, but... I have to say not even close to all, but from almost all to quite a few were by species. Some "dead" RT, some only "down" RT no matter what species. But all those hit were harvested if at all possible no matter how much extra effort it took. Some took a finishing shot and some didn't, some only made it a relatively sort distance away, some took tracking to find, a couple long tracking. I was raised by the standard that its all about ethics when hunting, your respect for the game itself and any you do chose to kill to do it as humanely as possible. Means I feel that what some might consider just lowly vermon still deserves a humane kill just as much as a big game animal does. So to me anyway that dictates taking the shots you are confident you can make, being willing to pass the iffy to very iffy ones where a poor hit can mean lost game that will probably suffer a slow death. Anybody that says they haven't made a bad shot hunting where they hit poorly, no matter how much experience they have is not being honest with themselves, or others. I have, quite a few by some standards, not so many if I consider the number of years and number of shots fired handgun hunting.
But I do have a dark side... and this is not an excuse for it. I give some leeway to hunting ethics when doing long range varmint hunting, simply because long experience doing it suggests it will either be a DRT hit or a clean miss "almost" all of the time. I also felt I had to give some leeway when doing ADC for landowners just for the use of their land, never for a fee. With most of them it's all about the numbers to retain their ADC, save them whatever damage is being caused, their expense for and even more collateral damage to other species if they have to poison. So if I felt confident I had a very good chance of connecting with a solid hit, even if it meant follows or tracking, I would take the shot. I take the plunge for the LR varmints and ADC knowing I will almost always be able to finish the job if needed with an immediate followup, where as with a poor hit on game animals often you may not get that opportunity immediately, or not at all. So me bad for sure in some P&V situations, but I always tried to be 100% ethical in all others. Over all those years it mattered not what others thought of my choice or the reasons why. Still doesn't, I chose my path, live with it just fine because it saved the landowners (and those that rely on their products) money, and even more important to me personally saved other species from the poison.
FWIW-YMMV