I could see it potentially working with a strict "story mode lockout" that means that, even if you've completed everything up to Lv70 in this mode, you can't participate in group content until you have also cleared that dungeon (and everything before it) in normal play mode as well. Perhaps it also stops you from finding gear and rare items in the dungeons.
Yes, this is an MMO, but it's also an installment in a series of usually-single-player games and has a heavy focus on story. "Just watch the scenes at the inn afterwards" is not really an option, because there may be additional story scenes after you've left the dungeon but before you can go to an inn, including non-cutscene dialogue that can't be revisited, and then you get everything out of order.
The first good example I can think of, having just cleared it with an alt charater, is Toto-Rak. Being able to go in there for the first time as a solo player would be a huge help - you could take your time, read the water-stained notes (not that they were particularly useful in the end), familiarise yourself with the complex layout, explore the side passages and take your time watching the actually quite long and important scene before the final boss battle. I skipped it this time but when I was really there as a new player, I watched it because it was clearly important, and yet I couldn't pay proper attention to it because I was worrying the whole time about making people wait. Likewise for the long scene at the start of the Bowl of Embers.
While it's currently a non-issue with the forced cutscenes, this was even moreso the issue with first-time players being rushed through the final dungeons. You couldn't simply skip through the scenes in the Praetorium and "watch them after" because it took you straight into the finale, the 'conclusion' scenes afterwards, and then into an in-game scene where everyone had something to say about what happened - and you can't replay that later. It's a one-time experience only, unless you take an alt character all the way through ARR again. (Even for the things that can be revisited, the inn cutscene book has that annoying element of only playing one scene at a time and then dumping you back out into the inn room, even when multiple scenes originally played one after the other.)
With the system as it is, the ten minutes of "free time" after beating the boss is the best opportunity for appreciating the dungeons for now, although it's not perfect. Depending on the location you might be able to complete your dungeon map and obtain additional treasure that everyone else skipped over - though this may involve 'suicide runs' into rooms full of monsters that you won't be able to beat alone - just target the treasure chest and open it before the enemies inevitably kill you. (I find that you can usually beat one monster alone with HP recovery and/or potions, maybe two if you're a healer or an arcanist/summoner using your tank pet, but a group of three is overwhelming. Tank pet can also be used as a brief decoy.) If you die at this point, you respawn at the final boss arena - so you may just be able to keep exploring, but some dungeons have one-way paths that you can't get out of again.