I agree that the plot of LMoP has more holes than Icespire Peak. But the gameplay, scenarios, and quests in LMoP are more varied and fun at the table, and present a more complete picture of 5E as a game. Icespire Peak is very heavy on combat and lighter on the other two pillars (especially roleplaying) whereas LMoP does a better job of incorporating all of them. Icespire Peak's Job Board is really uninspired, and too many (not all, but too many) of the jobs amount to "go there and kill stuff."
Icespire Peak is good for a beer-and-pretzels group that wants minimal role-playing and short episodic missions that can mostly be completed in under 3 hours - or for a DM looking to cannibalize it for side-quests for levels 1-6. And there's nothing wrong with that. But LMoP, particularly when run using the pre-gen character hooks, has at least some storytelling depth that will evolve naturally from playing it. Icespire really has no depth or characterization at all unless the DM works to overlay it onto a very generic set of scenarios.