You don't even need to be a math grad for it to be natural. It's just a natural way to perform set operations, pretty much everybody who knows a little bit of math is familiar with it. End even if you are not, you need like 5-10 minutes to learn it, and then maybe a couple of weeks of using it to become really fluent.
And I feel like "is not ASCII" is pretty silly complaint in 2020 anyways. First of, if these characters would be widely used in 1980, they would be on every keyboard today, same as it was on keyboards for APL. Second, you don't really have them to be literally ∀ and ∃, it could have been &A and &E for example, and then every other IDE, including some fancy product of JetBrains, vim & emacs and most likely even your mysql-cli (at least some wrapper around it written in Python) would turn them into pretty ∀ and ∃ on your screen, same as some editors do for λ.
And third, which is a personal pet peeve of mine (so I probably should keep my mouth shut about that, but I cannot): I really, really wish we'd stop with all this ASCII bullshit already. There's nothing special about ASCII except it's 7-bit. And that's outdated.
It may come as a shock to your average American, but most of the texts in the world are not ASCII, just deal with it. If your product doesn't support that, it probably means it's broken, outdated and will eventually lose to a competition, so you don't do yourself a favour forgetting about that.
And with regards to input, there's nothing complicated about typing ∀ (or anything else like that) on an ordinary US-layout keyboard. For me ∀ is 3 very fluent keystrokes. I use XCompose, which is a blessing, but other operating systems have similar software with similar capabilities as well. I understand that this is not something most people are familiar with, but that's just bad and shouldn't be respected: using a mouse also wasn't familiar to every single PC-user out there. With demand comes the supply.
So I really dream about the day when typing nice, clear syntax like ∀ instead of awkward Perl-like character sequences (to read which you need mentally traumatizing professional deformation and/or an IDE post-processor) becomes the norm of programming.