I'd argue the 95% of staring at something else is actually very harmful for fan engagement. The more the audience is being entertained by something else means less time you're the one entertaining them. Instant entertainment takes the edge off the game for us fans who are invested to the point of being mentally unwell (everyone here), but I don't think it's great for getting casuals invested. And yes, all sports probably have similar problems but I'd argue that the Instagram generation took their captive audience from them and it's basically showing off what we all already felt, that daily 3-hour sporting events are mostly high-sponsored filler content.
That said, I don't really include the Blue Jays franchise in struggling with fan engagement. The Rogers marketing teams are beasts and the Blue Jays are uniquely suited for a country-sized market. Doubt a lot of the other franchises could compare. Canada and the Blue Jays are probably one of the few markets MLB aren't concerned about anyway.