I think it's mainly availability. There are not that many folk out there developing burners. Those that are are presumably somewhere in the US, and Tweco are the biggest name there. If that's what they've used, they'll feel the need to put a caveat into any write-up to the effect that the proven design uses a Tweco 14t of a particular size and anyone deviating from the proven design is on their own. It really doesn't take much change to royally louse up a burner.
For what it's worth, I think the QC on the hole size, the tapered lead-in to the hole itself and the external taper are the most important things.
If you fit a choke, you can effectively deal with any variations on hole size by going down a tip size and choking the air appropriately.
Any variation in the lead-in profile will just change the discharge coefficient of the jet: You'll need a slightly higher or lower pressure for any given gas flow, but you'd only ever know if you had 2 burners side-by-side.
The external taper is probably THE most important thing. It looks to me like it will allow the air to mix more smoothly with the gas, where a squarer tip would cause much more turbulence.
I have used no-name MIG tips in burners without problems, but I was not working to somebody else's design. Over here, the DIY mini-migs have M5 threaded tips and 1/8" pipe thread to M5 reducing bushes are a standard pneumatic fitting, which makes things easy.