Am I the only one who considers non-armored cars to generally be wildly impractical for any part of this game? Both missions and free roam seem pretty unforgiving without one, and the Kuruma or the armored Schafter are both plenty fast for me.
Any heist mission that doesn't involve shooting from your vehicle is best done in the fastest vehicle available.
For example, any mission where you have to drive somewhere and switch to another vehicle (dinghy, sea shark, helicopter, bus, etc.).
Just to elaborate on this, using the Pacific Standard Heist (still the best money making method in the game) as an example:
Heist Setup 1 - Vans: I'll take my T20 for this. This mission involves no shooting and revolves around driving to all of the vans within a time limit.
Heist Setup 2 - Avi: I'll take my T20 for this. You want to get to the Seasharks (I use the Northernmost ones) as quickly as possible, and having a fast vehicle available for the drive back to the final objective (and for eluding the police) helps tremendously too.
Heist Setup 3 - Hack: If I'm the driver rather than a decoy, I'll take my T20 in order to get to Lester's factory as quickly as possible to pick up the van.
Beyond that, there's always races as well. Racing is a lot of fun in this game, it's actually fairly underrated as an arcade racer if you ask me.
Then of course there are the various free roam events that call for fast cars (highest speed, longest jump, etc.).
If you're in your apartment and order a Pegasus vehicle to be delivered, you'll generally want the fastest vehicle possible to get to wherever it spawns as quickly as possible.
Finally, if you play in passive mode (as I often do), then speed is often more important in a vehicle than bullet or explosive resistance.
So if you're wondering whether you should buy a fast car like the T20, then those are some of the uses it would have.