I'm all for it. Some nations utilize (or have in the past) mounted 60mm breech fired mortars for upping turreted firepower on vehicles and boats. In US circles, tracked AFVs are purpose designed as mortar carriers and we have moved almost exclusively to 120mm mortars for those vehicles. I've seen Stryker wheeled AFV mortar carriers that use both 81s and 120s (one or the other).
The idea being that a 60mm is just too small to justify wrapping an armored vehicle around it... when you can carry heavier, longer ranged, more capable 120mm cannons with the same vehicle instead. You couldn't even see over the top of a mortar carrier's side armor with a little 60mm mounted inside. Which makes it kinda difficult to use artillery sights or lay in a gun. While 60mm mortars are a foot portable marvel, 120mm is a whole 'nother class of truly heavy fire capability and range. The big boys employ the smaller mortars (60 or 81) as essentially BUGs for ground mounted use.
Mortar Carrier AFVs give mortar crews the ability to shoot and scoot (while under armor protection) in a counter battery fire artillery environment. One where the enemy is likely to rapidly saturate the radar identified mortar firing point of origin. They also provide integrated comms/FDC computers, vehicular mounted night vision, a shelter for the crew, & crew served support fire from vehicular mounted machine guns. High angle indirect fire able to keep up with mounted infantry. The few times I got to work with mechanized mortar platoons, I was envious of their ability to haul ammo, rapidly emplace/displace, and cover ground. Of course, the flip side is that they are big targets that can't just traverse all terrain. Big targets attract big enemy munitions.
I've seen some smaller off road wheeled vehicles / all-terrain buggies proffered by various defense firms over the years. Designed to full-time mount smaller mortars. But I'm not sure who has actually adopted them. A 60mm mortar can be thrown into a sub compact car and then transported. The trick is to field a vehicle that mounts the cannon full time on a rotating plate able to absorb recoil while also providing enough traverse and range of elevation for the guns employment.
50mm -60mm mortars excel at being man portable firepower. "Poor Man's Artillery". If you spend money to field AFVs, it makes more sense to maximize throw weight and range by going with a larger mortar system. Because AFVs can readily handle moving the bigger stuff around the battlefield... while foot infantry can't.