Well here is that 2019 Kona bike count list from Triathlete Mag

Cervelo – 489
Trek – 258
Felt – 190
Specialized – 184
Canyon – 179
Quintana Roo – 122
Argon 18 – 117
Scott – 103
Giant – 84
BMC – 77
Ceepo – 65
Cannondale – 47
Ventum – 43
Liv – 32
Dimond – 24
Cube – 23
Orbea – 20
Fuji – 18
BH – 10
Pinarello, Simplon, LOOK, Ridley, Airsteem – 9
Willier, Kestrel, Planet X, Factor – 8
Parlee, Factor, Merida – 7
Stevens – 6
Kuota, Boardmann, Blue – 5
Storck, Rose, Guru, Garneau, Rose, Colnago – 4
Litespeed, Diamondback – 3
TriRig, Premier, Squad, Anchor, Cuierciotti, DeRosa, Pardus, Sopta – 2
Jamis, Epoca, Aerocat, Spinaro, Pacer, DEAD, Issac, ADR, Nodo, Softride, Java, Kemo, Piton, Serotta, Avacon, Silverback, Dolan, Griffen, Avanti, Dolan, Anderson – 1

What explains the demise of old tri brands like Kestrel and Litespeed?

Litespeed is part of ABG with QR so they don't have their brands competing with each other. QR is Tri and Litespeed is everything else.

Kestrel was part of ASE, who stopped investing in R&D for that brand (focused on Fuji). The last bike they released is open mould. ASE went bankrupt - not sure what the new owners are going to do with the brand.

I’m surprised more lower listed brands don’t push discounted sales to qualifiers. I know some will give you a bit of a deal, but not many.

I think one oddity specific to Kona is the high level of profamateur athletes who have some level of bike sponsorship. You get seemingly random brand names thrown into the mix and they may only be re-spray frames anyways. There was another thread on the main page that highlighted Trek had more bars than bikes at Kona. I am will to bet this is because people were riding re-badged Speed Concepts with some random sponsor name on the frame but with Bontrager still clearly visible on the bar. To my knowledge TriRig and Premiere don't have a lot of 'team sponsorship' deals which drive purchases of the more niche brands at Kona. They are also pretty expensive options if the goal is to strip and paint and cover them in sponsor logos. Finally the numbers probably are about proportional to Canyon when corrected for total sales/market sales.

Based on the number or TriRig component I saw on TT bikes at the World Championships they are clearly doing things right and don't need to be throwing money at getting more Omni's at Kona. If I was Premiere I would take confidence in the rise in Canyon and try and get a few more bikes under athletes given this seems to be working for Canyon. Canyon has a ridiculous marketing budget and Premiere certainly doesn't need to try and compete but they do need to distinguish themselves from the other brands you highlighted.