Sure, the voltage divider works ... if the load impedance is high. Not a good idea for a 50 Ω load.
Op amp needs a dual-rail power supply, so it needs some auxiliary power, then power electronics to get both rails. Stuff starts to get complicated, and now that $1500 Keysight box starts to looks worth its price...
This. A function generator is not a trivial piece of digital electronics. It's a complex, highly analog beast, where the digital component of the circuit is actually rather small. Nowadays a dedicated IC (such as the XR2206) is the starting point for a home-made FG.
I'd even argue that the XR2206 is pretty obsolete when it comes to function generation methodologies.
For one thing, it's very limited in frequency - 1MHz max, and dependent on analog components to generate it.
For another thing, it's really limited in waveform types. Practically, you can only generate sine, triangle, and square waves. Modulation is possible, but requires extra hardware to pull off.
The advantage I see of the DDS is that, once the signal generation portion of the product is software based, you can push upgrades to functionality via software updates. Not something any XR2206 can do!
Op amp needs a dual-rail power supply, so it needs some auxiliary power, then power electronics to get both rails. Stuff starts to get complicated, and now that $1500 Keysight box starts to looks worth its price...