It’s a big mistake to underestimate the extent of human folly. I’d easily believe several whole crosses were sold and thousands of fragments sold, resold, donated to kings to curry favor etc. A fool who parted with his money stupidly may try to discreetly dispose of the evidence.
Whatever we might or might not 'easily believe' - the only data points that we actually have are that the known splinters of the true cross would easily fit into a shoebox
It's going-home time here. Hope you all have a glorious weekend.