This is the norm in the software industry. As grunts or lower management getting tasked with the impossible, saying "yes" and doing "maybe" is really the only way. What they (upper management) gonna do, fix it themselves?
And then, of course, for the PM's and upper management layers, the fact that their project "met the date" is what is measured and congratulated all around. The product could be a stinking pile of XXXX, but "it met the date", so they get their kudo's, their bonuses, and the devs. and users are left with "stinking pile of XXXX".
About ten years ago I had the option of taking the red or the blue pill. I took the Windows pill by mistake.
Or maybe I just blame capitalism, haha. No deadlines! I do this because I like it!
Yes, they should have. adding tests long after the fact is next to impossible because, when you spend a long time not adding them, your codebase tends to degenerate into an untestable mess. One of the key benefits of strict TDD is that you feel the pain of testing your code before you write it, so your code is testable from the start.