On all the agile projects I’ve worked on, the teams have been very reluctant to make a specification in place before starting development.

I don't think this is an Agile thing, at all. I mean, look at what Agile's main trait: multiple iterations with acceptance testing and product&design reviews. At each iteration there is planning. At each planning session you review/create tickets tracking goals and tasks. This makes it abundantly clear that Agile is based in your ability to plan for the long term but break/adapt progress into multiple short-term plans.

For your sake, I hope your employment was agile as well. Those jobs sound like they were dumpster fires waiting to happen.

That's boneheaded.

How did they know how to break things down into tasks? How did they know if a task would fit in a sprint? 😄