Yes, all the people who would complete the dungeon in time would do so, which starts out great, but inevitably, because the slower groups take longer, even if some quick groups got in right as the servers came up after the maintenance to alter/remove the time limits, all the slots freed up after the quick groups are done have a chance to be filled with a slow group instead of another fast one, with the occasional bump when a quicker group happens to get in line. In the end you'd have more slow groups than fast groups in progress at any one time, meaning longer wait times.
In-progress is great, but unless you're saying that there's enough people having to drop out of their groups at all times that in-progress is a guaranteed instant-queue for all the people waiting outside, even that will only carry you so far. Not having time limits may not have ended WoW, but I certainly don't see having them being the end of Eorzea, especially with the options available, dismissed or not.