Their point is that there is actually a very large amount of duplicate effort is happening now, as everyone separately goes for the first ideas: this makes it more probable that a lot of effort will be wasted on super-duper-triple confirming that the first thing everyone thought of didn't work, slowing the exploration of more nuanced ideas.
But besides waste of time and resources, the only other problem they mention is an increase of false positives. These naturally become more common as you try the same thing more often unless you correct for it by keeping track of all the other trials.
My problem is that there are too many inconclusive trial. Someone makes a small trial without a control group, so the result is promising but difficult to interpret. Someone else makes a small trial without a control group, so the result is promising but difficult to interpret. Another person makes a small test without a control group, so the result is promising but difficult to interpret. ...
So after a few months, we only have promising inconclusive results.
Not that all the trials are different, so it is difficult to compare them. IIRC There was a recent trial with remdesivir without good results, but they only tried the drug in patients with strong symptoms. So people asked what happens if they use the drug in the beginning of the infection.
But besides waste of time and resources, the only other problem they mention is an increase of false positives. These naturally become more common as you try the same thing more often unless you correct for it by keeping track of all the other trials.