Their only chance to return all funds to every owner was to continue trading, coz their value alone is not enough
If you'll recall, the original version was that Mt. Gox was hacked for 950,000 BTC. 100,000 of which supposedly belonged to CEO Mark Karpels. That left 850,000 of the hacked bitcoins that allegedly belonged to Mt. Gox depositors.
Next Mt. Gox claimed that it had "found" 200,000 BTC in an "old-format" wallet, so really only 650,000 of depositors' bitcoins had disappeared. Though, what actual proof exists that these supposed 650,000 bitcoins actually ever existed? Perhaps there were never more than 200,000 bitcoins in Mt. Gox in the first place, in which case, absolutely zero are now missing.
Doesn't it seem like a little bit of a stretch to you that a 28 year old who had been in business for about 3 years had amassed 950,000 bitcoins worth some $500,000,000? I know pizza used to go for 1,000 BTC per slice, but that's simply absurd. That Mt. Gox ever even held 200,000 BTC still seems very hard to swallow, yet is at least possible.