They all do. It isn't always a discrete chip though. Like in the case of a MicroSD the memory and controller is all integrated. You can open up some full size SD cards though and the memory and controller will be separate chips.
Because I can regularly find 64GB cards at reputable sellers for about $10, I no longer format cards. I shoot until they are full (backing up as I go). When a card is full, I "file" it. Basically, I've started treating memory cards as "digital film". I know they are likely to degrade over the years, but formatting guarantees "degradation" right now in the present. [1] Compared to film, SD cards are cheap. Not zero cost, but @ 40 RAW images per GB, it's only a fraction of a penny per shot. With .jpg it's a fraction of a fraction of a penny.
[1]: It also opens the door for accidental formats.
With modern TLC flash any card without wear leveling would fail pretty quickly.
Wear leveling is actually a major problem for applications where power might be suddenly cut, because if it happens while the wear leveling is running then the block allocation table can be corrupted which leaves the whole card unreadable. It's a pretty common complaint among i.e. raspberry pi users who tend to unplug them without shutting down.
