The Ninja Turtles/Batman comics and MKvsDC are Mario & Sonic type of crossovers. Just because they've crossed over with DC in the past doesn't make them a part of the DC Universe. Otherwise all the different characters in Smash would all be considered Mario characters. DC comics has built it's world out of different heroes meeting so Batman and Superman meeting isn't as much of a crossover. But non-comic characters that DC didn't create and characters owned by rival publishers would be a weird crossover when they meet DC characters. So a DC universe game like Injustice shouldn't be having non-DC characters, especially when the guests are exclusive to DLC. But Smash could have any character because the crossover aspect is the main draw of the game. "Infinity War is the most ambitious crossover event?" Please, Infinity War isn't a crossover, it just uses characters from spin-offs of Iron Man. Meanwhile, Smash Ultimate is a true crossover because it has unrelated characters from different universes meet up.
Injustice isn’t a crossover, I can agree with that, but that doesn’t mean it can’t have some crossover elements. Non-DC characters add to the roster and most feel natural in the game. I think Injustice can work like Smash, if they’ve had a history with DC then they could work.
To start MK actually has comics published by DC since Warner Bros. owns both. Also, the only reason we have Injustice is due to the crossover between MK and DC. DC’s fighting game side is because of Mortal Kombat, and the characters surprisingly work well together, mainly the MK ninjas like Scorpion and Sub-Zero. They feel pretty natural around DC characters now, and since DC has already established the multiverse and different Earths, it makes the crossover possible and not very weird.
Hellboy is a comic character, and is now getting movies made by WB, so DC and Dark Horse aren’t really competing. The two companies seem pretty chill with each other, sort of like Nintendo and Microsoft right now, so it’s like they’re competing, but really they’re just working together to take down the other company, ie Marvel. Again, he fits due to the Earths and such. The same applies to Ninja Turtles.
I will say, the crossover characters could have been better though if they were willing to go crazy. The franchises could have been ones that established themselves well in the DC Universe. Well my suggestion may seem strange, I think Looney Tunes and Scooby Doo would have been better picks. Scooby Doo has crossed over with DC so much that they have basically been integrated into the universe. DC characters know of them and they know characters like Batman. They’ve teamed up with the super heroes and gone against villains so many times that I think they would have fit better. As for Looney Tunes, well Daffy has become a full member of the Lantern core before and the Toons have crossed over into the DC Universe before with Bugs and Superman, Lex and Porky, Marvin taking down the Green Lanterns, Taz and Wonder Woman, and others.