The way I see it, there's a huge misconception about CAPE about lots of people, including yourself with no insult intended there.
That is more than enough to produce a major tor outbreak given thermodynamic profiles. If you have strong height falls and cells able to sustain themselves, yeah. Meteorology is a rare case of where more will mean less. I have never seen a major outbreak in 5k+ CAPE because the more water-loaded profiles are, cells rarely organise a consolidated mesocyclone. You can get the most viciously violent tornadoes in extremely high CAPE when the factors are there. I think there's enough to garner what tornado I mean in Texas by that. But around 1.5k to 3.5k is the gold standard for a outbreak with several long tracked supercells. There's a perfect balance, reliant on thermodynamic factors and etc.
@jiharris0220 has said this. Shear will always BE the true factor of tornadoes. The rare cases where it matters is boundaries like Dickens last year but if you think about it, those boundaries also create localised extreme shear. It can work eitherway. A better example of HSLC EF3+ tors would likely be
Leap Day 2012, Harrisburg, IL
03/02/12, West Liberty
Cookeville.
How did all these cases work? HSLC high end tors usually rely on supercells maturing thru the environment and being able to sustain well ahead of a very intense LLJ. These cases and their supercells initiated hours beforehand. Does it always work? No. But today isn't a example of that. Convection from polo will streamroll the area with likely flooding as well as limiting instability. These supercells did initiate in over 1k CAPE but as CAPE decreased, the cells were essentially their own forcing mechanism by managing to push thru via longevity and maturity.
This is meant to be moreso a quick checkup on what is actually considered reasonable CAPE for these setups. 4/27 produced major tornadoes into the night with less than 1k CAPE and why? Because those supercells, the same ones that produced HPC and Smithville had persisted so incredibly long. It's tricky to forecast these situations.
Lesson done.