What games? Because whilst titles such as Splatoon 2, Smash Bros, Fortnite, etc exist they're not exactly in the same ball-park as Call of Duty which is a modern high-end AAA title with constant gigabyte-large updates and an online system that relies heavily on features that the Switch doesn't support atm (parties, streaming capability, etc). Perhaps the only 'modern GaaS' title on Switch that isn't F2P is MK11 and that's a 1-on-1 fighter not a team-based multiplayer shooter like CoD.
As for storage space, it definitely would because modern CoD games can go into the 100+gb range, and BO4 went there at launch, and that's without many pre-rendered cutscenes and other 'easy-to-cut-down' things. They'd have to get a team dedicated to compressing and downsizing the game's assets for a console that simply won't get all that much revenue comparatively. CoD is already a game that's putting its teams at the breaking point so that's definitely a big ask.