I still think it’s a matter of your personal preferences and priorities, even under your circumstances.
I consider a morning shower as essential to my day-starting mindset as breakfast and a cup of coffee. It definitely has an impact on how effective I am at being productive throughout my day — or at the very least it has an impact on my perception of how effective I am at being productive. And that matters to me.
One reason is that I seem to be generally more oily and sweaty than the average person. I know I will not be as presentable in public as I like to be through most of the day if I don’t take a shower in the morning. That affects my mindset.
Keeping my face relatively clean-shaven until 5 p.m. is another priority for me, and I always shave in the shower.
So if my shower routine suddenly required 40 to 60 minutes instead of the 10 or 15 it requires now, I would still prefer building that time into my morning routine. Maybe eventually I would reassess and find a rationale for a different approach based on lack of sleep, when I can reasonably expect to get to bed each night, how formal I feel my workplace requires me to be, etc. But my default would be to try to make it work in the morning because of how I prefer to feel when I leave the house.
Obviously only you can decide how important that would be to you.