The problem is that any "leeway" will be taken up by cheaters. And the cheaters far outnumber the people like you who genuinely need some slack.
When I taught, I tried not to be dogmatic. But people have to understand that when a prof gives leeway, he's putting his ass on the line ... he doesn't have authority to do that and he could get burned if someone gets riled up about it.
So, if your prof cuts you slack that you needed, keep it to yourself and STFU.
Citation needed.
I suggest reading "Human Kind" by Ruther Bregman, which is an interesting (and substantiated) counterargument to this idea.
My class.
Quote from student: "Thanks for having the best class."
Reponse from me: "Best?! You're getting clobbered in my class."
Quote from student: "Yeah, I'm not doing that well, but the bullshitters who always manage to butter up the Professor and skate through are actually failing for the first time ever. Everybody knows where they stand in your class. And, they know that if they put in the work they get the grade and if they don't, well, they get hammered."
Response from me: "Thanks, I guess?"
I considered it a compliment only because my father who taught high school for almost 4 decades said: "You're teaching a class. The students have to think you know your material, and they have to think you are fair. Nothing more. If they like you and/or respect you, so be it ... but those are non-goals. Your goal is to teach them the material, not be their friend."
Instead of being able to make a judgement call or respond appropriately to changing circumstances; instead of being relied upon for your ability to judge the needs of your students accurately, you risk being flagged up for not sticking to protocol in matters of ~student~ consumer interaction.
If a cheater slips through, does it matter, that much, if the cheating is getting an extra few days of time to complete an assignment?
Aren't universities meant to be about expanding knowledge, places of learning? Aren't we making a mockery of the whole idea of tertiary education getting so caught up in catching 'consumers' gaming the system and the risk debasing 'consumer currency points' or exam scores in order to justify the busywork of admin departments? Software and software enabled culture is incredibly powerful but it also removes human factors and discretion and has made many things worse.
Pre-COVID, schools shut down for other reasons, like snow days. Doesn't seem much different.