Dota has sandbox because the game is well designed and built on a proper engine so that they don't even have to do anything extra to get sandbox mode features. The sandbox features Dota players use like refreshing cooldowns, having no cooldowns, giving gold and experience, etc are the same sandbox features the developers had originally built for themselves to aid them in development and testing. If you're a developer creating a new hero it only makes sense to have a built in way to remove cooldowns, a simple switch you could flip to make testing easier. And because Dota is using Source, those internally developed features are easily exposed to players, because they are implemented as engine configuration settings accessible through the use of the console.

For example, suppose when someone was working on Dota and wanted a way to let's say disable the fog of war because it would help them test, they implemented it as a Source engine setting like a "dota_all_vision_enable" command that could be turned off and on. So when they're developing and running their own development server and wanted to see what the map was like, they'd be able to enter the command dota_all_vision_enable into the console to test it. But since they've created a console command, they can just make it public for players to use as well.

Clearly LoL's engine doesn't have the same thing, so even if Riot engineers have their own internal developer sandbox (which we know they do, because they clearly use some sort of sandbox thing for their spotlights), they can't automatically present that as a mode to players on its own. They may already have their own private developer sandbox for their own internal testing but then they would have to build a separate public sandbox, because their private developer sandbox isn't suitable for public use. In Dota that's not the case, because sandbox is just the result of entering commands into the console to tell the engine to behave in a certain way. They are commands the developers already created for themselves that they use to internally test things themselves.

Riot has to think at the "game mode" level because their engine can't be changed as easily as Source can, while Valve can easily think and work at the engine level. This is all evident based on the way Dota handles their "sandbox" and how Riot is thinking about sandbox. Riot talks about it as a separate game mode, while for Valve it's simply them giving players the same access to what's under the hood (the Source developer console) and letting them flip whatever switches have been made public.