Independent replications of experiment (and the corresponding independent reports of observations) are a crucial part of the scientific method, no matter how much you wish it wasn't. Nature doesn't care if it is inconvenient for you to discover her secrets, or that it is more difficult for you to hype up your findings to the unsuspecting public.
There is a lot of transparency there, a lot of well meaning people with a lot of oversight.
I suggest most would admit 'there could be a problem' there, but it's out in the open if there is.
The problem of lack of repeatability I think has to do with subconscious bias on the part of the experimenters which will be less pronounced when there are 5000 people working on it.
On the other hand, there are many other experiments that are repeated billions+ times a day in order for consumer electronics to work, etc.