What you are describing is entirely reasonable, but again still a lightweight Agile process. The thing that I don't understand is what the people want who keep complaining about all Agile, not just (rigid) Scrum in particular. I've worked with XP, Scrum, Kanban and versions of those adjusted to particular teams and companies. If someone doesn't want any Agile and doesn't want Waterfall, wtf do they want?