Civ doesn't have menu driven combat, but especially early Civ games have super menu based everything else. Towns are the big highlight, but research trees, diplomacy, Advisors (lol) and generally all navigation until you learn hotkeys are very menu driven.
I would also consider a large portion of HoMM to be menu based for similar things. Basic movement and direct combat blissfully are not though with a standard interactive point and click interface. (Do we even try to call it by the rebranded Might and Magic Heroes? It doesn't roll off the tongue as well and MMH looks like a lame version of MMA).
The thing 4x avoids with its menus that JRPGs fall trap to is nested menus. Pick what you want to do, pick what type of thing you want to do that you chose to do. Use an item, pick what item you want to use, pick who you want to use that item on. It kind of doesn't if you consider Towns as a specific menu, but I think that is overly abstracting the implementation.
I don't mind me some menu driven combat and clearly like JRPGs that are coming out even now still, but menu implementation hasn't been a particularly strong point for years and more complex Western stuff falls prey to it as well (sup Neverwinter Nights? I heard you like radial menus so I put radial menus in your radial menus so you can menu while you menu). By coopting other genres combat systems Western stuff hasn't really solved UI design issues so much as side stepped them as they got better at it (Sup Mass Effect 1? I heard you wanted gunz so I got you 10 levels of 20 different brands of gunz for 4 different types of gunz).
There is solutions to it that kind of work. As much as I kind of loathe it myself, the wheel that Persona 3/4 (and 2?) used kind of works to remove some of the drudgery. It is still a menu but icons instead of raw text go a ways and cuts down on screen real estate compared to Final Fantasy's big bars everywhere (with added kludge in the top right corner for FF13 or your map and compass for FF12 if I am remembering right). I prefer the BoF 3/4 or Wild Arms directional inputs. It is still super menu based, but it really cuts down on the button presses at the macro level of the menus so makes it that much less intrusive and adds more muscle memory being able to be used in your menus. Bonus points if your menu can be used one handed by having at least L1/2 be at the very least Accept. Not that I want specifically less interactive menus, but if your menu driven combat system requires two hands to use? Good gods that is over the top. That would be like having to use a keyboard in a point and click adventure game. You have a perfectly functional input system in one place. Sure let you use X to accept or whatever, but don't neglect the shoulder buttons as perfectly decent inputs.
