The biggest problem, IMO, is that if you buy from a third party when shit hits the fan you have to rely on that third party. This is still a problem even with reputable travel agents like Amex and Chase. Even in the best case scenario where the agent is actually good, having to get a flight changed via a phone call with some agent who might or might not answer promptly and might or might not be able to work quick enough to win a race of rebooking after a cancelled flight before next best one fills up is just asking for a horrible experience. If you book with the airline directly they have a lot more leeway and power to unfuck your situation promptly.

Save your points and use them on hotels instead, where the experience is just as risky, but at least fails in a less spectacular way when it goes wrong e.g. unless you're booking with an agent in a high demand area where there are NO hotels you usually can leverage a backup plan a lot easier than if you are stuck in an airport.