Explain a recent prevailing hypothesis for why genomes like ours (and also plants, for example) might tolerate such large amounts of "junk".

Richard Dawkins wrote about 'Junk DNA' or non-coding DNA in his book 'The Selfish Gene'. The essence of the hypothesis is that this DNA merely exists to replicate itself, with no discernable biological function, and it merely 'hitches a ride' in the genome. Susumu Ohno hypothesised that mammal genomes could not have more than 30,000 loci under selection before mutation at the accepted mutation rate would result in a decline in fitness, so, for the large part, much of the additional genetic material can be regarded as 'junk DNA'. Ohno also observed that even closely related species have widely different genome sizes. So the answer to this question is that 'Junk DNA' or non-coding DNA is never translated into proteins and has no function in an organism besides some hypothesised regulatory functions.