Since you seem to have missed it, I'll point you to my first post in response to Rongway on this:
What I think I missed that's more pertinent here is that 'tension' I'm referring to is consequence. Yes, the AF/UI timer is an explicit punishment mechanic. That's the point. It's designed to keep you on the rails and guide players towards the core rotation and the ways in which you're allowed to flex around it. MP is not enough to enforce that. The consequence for screwing up your AF management is you lose your partially charged Polyglot. The Fire IV loss from Enochian is being removed in Endwalker, and you know what the punishment for that used to be? Dropping Enochian's buff itself, which was its own timer that couldn't be refreshed consistently, creating even less flexibility compared to now.
And unlike other mechanics that set your rotation on rails (Combos, Buffs/Debuffs with 100% uptime, Long cooldown GCDs) it still allows as much flexibility as the timer itself allows. BLM has a priority rotation where your goal is to cast as many Fire IVs as possible and the timer is the only thing that prevents you from doing that. You have to build in an entire new mechanic in order to justify its replacement, that's harder to explain, and even harder to implement with the same level of flexibility and readability. And for what, exactly? Not being able to drop it during downtime?
Well, really, what it's actually there to prevent is Chad McThunderhax from spamming Thundercloud a potentially infinite number of times in a row while maintaining AF3 the entire time. While the obvious use of the timer is it forces you to use F1 and potentially Sharpcast/Firestarter F3 to maintain your Fire IV access in the first place, it also serves as check on unecessary nonsense like that. Sure, that particular scenario is unrealistic and the numbers are worse than Ice Mage in practice, the fact is it serves as a guide to the core priority rotation and all of its variations.
To look at it from another perspective, since you're focused on downtime, we could ask "Why don't we just fix the downtime instead?". Imagine that in Endwalker all instances of Down for The Count and similar debuffs freeze your rotation timers for their duration. Cooldowns. Buffs, debuffs, whatever. All of it on-pause. What happens then? Well, the consequence of that is you're not losing anything during the cutscene, while the jobs that gain an advantage from downtime no longer gain that advantage. You might be hurrahing that you finally can cut your losses, but I see that as a net negative. Precisely because it equalizes jobs rather than allowing situational advantages and quirks. One of BLM's advantages is it has the highest potential DPS in the game. And the costs of that is its floor is one of the lowest if you don't understand it. The AF/UI timer is only one facet of that, but it makes micromanaging its movement more interesting and rewarding without being too difficult to understand. I'd argue all the Ice Heart, AF stacks, Paradox, and Polyglot nonsense clogging up their Job Gauge is what causes it to be 'difficult', but the more accurate term is bloated.
All in all, while I understand the sentiment, I do not think removing the timer is good for mechanical diversity nor from a design elegance standpoint. And, frankly speaking, we already are struggling for that in multiple jobs across the board. If you don't like it, I'd advise you play a different class that gets something from downtime in instances that make that uncomfortable for you. I for one will level the job, suck at it, and listen to my static enjoy it for what it is content in the knowledge it doesn't need that kind of reductive attention.