The impact of tubing sizes

[Fiber9]

You push the tubing into a hole. There is a collet lock that surrounds and grips the tubing so you can't pull the tubing out unless you release the collet lock, and an O-ring that squishes between the inside of the hole and the outside of the tubing, creating a seal.

What makes push-fit fittings so good is that there's nothing blocking the entrance/exit of the tubing. It's not like tubing squished over a barb where the liquid has to squish through the smaller barb orifice. With push-fit/quick-fit fittings there's nothing obstructing the flow at all.

Cathar, the push-fit or Plug&Cool aren't to my knowledge all round on the interior.
For example the Legris LF3000 (used in Europe), are hexagonal on the inside, and still cause a restriction.
The g1/4 BSPP for 10/8 tubing push-fit is 7mm at the end, and as you move to bigger tubing, say 3/8 or 1/2, the difference between tubing diameter and the push-fit is bigger, because it still is 7mm at the end.
The only way to make them equal to the tubing inner diameter is to ream (porting) them.
Being the case, the only tubing diameter that makes sense and can truly match the diameters of the tubing with the diameter of the push-fit is the 5/16 or 8mm ID.
Then as you have to use rigid tubing, you can't use the softer Tygon, due to the differences in the wall thickness.
You can still use Tygon and Push-fit with a barbed connector, but in this case if you use the barbed connector below, as Swiftech you still have a restriction, because it's just a barb with all the inconveniences it has.

Finally if you use the tube inserts, there's also a restriction.

Edit: You might have a look upon the Jonh Guest parts , altough I don't know if they have the same characteristics as the Legris parts.