Front inserts are common for clay/dirt:
https://rawspeedrc.com/radar-2wd-front-buggy-tires-w-inserts-2-2-1-pr/
but carpet/turf they are typically a smaller profile without an insert:
https://rawspeedrc.com/fast-forward-2wf-buggy-carpet-tire-no-inserts-1-pr/
It really comes down to preference and tire design which can change from one manufacturer to the next. Softer compound rubber designed for dirt to get more grip will need an insert to support the tire where harder compound rubber designed for carpet doesn't need the support, though I have seen folks install inserts on front carpet wheels to take away some grip to make the car easier to drive.
Not really sure if the DT03 will get enough speed to make much difference either with or without inserts... shrug