Generally. Most IP's that are popular enough to be worth adapting have done enough world-building that it's not that hard to make a story that actually fits into the universe and forms a plausible part of the series. The Mario Bros movie was very much not a good adaptation, and part of that can be blamed on the fact that there's really no actual story to work with in Mario games (especially in 1993), but Mario RPG, Paper Mario, and M&L games have all shown that it's perfectly possible to tell an actual story without reinventing the universe. There's no reason a movie can't do the same.
Studios' repeated failure to do that is not because it's impossible, it's because they'd rather just shoehorn a pre-existing story template into the IP they purchased and hope that brand recognition is enough to carry it to profitability.
Actually, the reason the Mario Bros has such a weird ass story is because of the dumbass directors, not the fact that they had no story to work with: