Honestly to remove strict MSQ requirements would help the game more than it would hurt... Players that are interested in the MSQ will do it anyway and players that aren't would probably do it if SE would give a shiny achievement for completing the MSQ.
Because we have to keep in mind that FFXIV only remains a success if SE can attract new players. There will be enough new players that wouldn't mind questing through all MSQ but I bet the bigger part would get turned off by it - either because they're used to skip from other games or because they don't care about the story or because they wan't to play with everyone else ...
Imagine how many new players will start with Shadowbringers that have no clue that the product they bought is not accessable unless they quest for around 3 weeks or pay even more money. We will lose a lot of potential new players - players that might have gotten be your friends but will never be because of the unneccassary grind.
With adding New Game+ players that want to relive the story (or do it for the first time) will do that. But SE should give new players the possibility to start in an expansion like the veterans (without paying twice for it). And to be fair it doesn't effect our gameplay if dungeons, trials or raids get gated behind MSQ or not - most of them are already hidden in side-quests independant from MSQ.