I wonder if in that case, there are exceptions made for people without the ETA who did not expect to be delayed? Anyone know?
It is not an issue. You really have two options. First, you could go on the app and fill out the form. Per the guidance of the UK, you need not be approved, only have applied. (Though for most, approval is immediate).
The second option is you merely talk to an actual person, as opposed to using the e-gates. I suppose you answer pretty much the same questions, and that person simply "approves" you for entry.
If you note, there have not been widespread reports of people turned away from the border, or held in limbo for not having an ETA...and the process has been in effect for over a month. Since airlines are not required to verify that passengers have an ETA, I can imagine any number of people turn up at the border daily without an ETA.