[I]t will not always be obvious that it is an advert
Super-illegal over here...
There's nothing preventing you from running an agile project with a robust and complete design. Agility allows you to pivot if and when required.
The easiest way to think of agile projects is a series of really small waterfall-like mini-projects that deliver a working product at the end. As you complete each mini-project, your product comprises a larger set of features. When your feature set reaches MVP, you can release or continue iterating to complete more features, but you can feasibly release at the end of any mini-project.
All of the arguments I've seen around [Aa]gile have shown that both sides are unwilling to concede that they don't actually understand the others' points of view.
There is no project that can't benefit from the ideas agile project management introduces, and there's no rule that says you should throw away your working model to implement agile (although it is generally easier to start with a single team that does start from scratch).
ALL projects benefit from measuring the outcomes of small, incremental changes and continually finding and limiting waste.
Top Ten Things Overheard At The ANSI C Draft Committee Meetings: (6) Them bats is smart; they use radar.