I'd say the best example of all came fairly late in the PS1-era.
Namco made it a point to show people the difference between 30fps and 60fps with the bonus disc that came with R4: Ridge Racer Type 4.
On the disc they gave us some notes about the development of R4 and how they decided that only 30fps was possible for that game with all the graphical advancements they made.
However, in their notes, they said something like their R&D did not goto waste. Part of the engine / testbed was used to make a graphically improved version of the first RR at 60fps.
They included a demo of the original 1994 30fps PS1 port and a demo of RR at 60fps with improved shading, textures.
This was called Ridge Racer Turbo Mode, or the Ridge Racer Hi-Spec Demo, depending on the territory.
Edit: Namco's notes from R4's bonus disc
This was the PS1-N64 era. It would have been a lot less remarkable if Namco or any dev had done something
like this during the PS2 era, with all the extra power consoles of that gen had.
So those of you who have a complete R4, go ahead get that 2nd disc out and play in on a PS1 / PSone (rather than the backward compatible PS2 just so do don't start to
think for a second the higher framerate is because of PS2 greater performance, even tho it's not).
With that said, with modern HD consoles, starting with the Xbox 360 forward, there are many reasons why devs choose to target 30fps for most games. More impressive graphics will sell a game far more than a higher framerate will. Better graphics are more instantly impressive to the majority of people buying games.
30fps is just fine for many types of games. The amount of things Rockstar is adding to the upcoming Grand Theft Auto V remaster on current consoles would not be possible at 60fps, even on PS4.
The traffic, oh look at all that traffic