For a starter:
SAS is more Danish and Swedish than Norwegian. The biggest SAS hub by a big margin is Copenhagen, not Oslo.
TUI Nordic is a Swedish holiday-charter airline, they are not Norwegian. They have a fleet of only 3 aircraft, and my understanding is that they do more work out of Sweden and Denmark than Norway. Pre-Covid, Danish JetTime did most of the flying for them.
Norway is a long, mountainous country filled with fjords and lakes. Driving anywhere takes forever. Building rail lines is expensive because you have to tunnel and bridge most of the way. The only practical ways are by ferry or plane. That explains Widerøe and much of the SAS operation in Norway. It should also be pointed out that for many years Widerøe subcontracted for SAS, and was even owned by SAS for a while. Widerøe also does the really small turboprop stuff, which all the others barely touch. Widerøe also has a lot of PSO routes.
Norway's geography is a good point and I'm sure Norway relies more on flying than many other countries so may be the primary answer to my question.
Norway may be SAS's smallest home country but SAS and Norwegian both do already compete on number of domestic routes so it's interesting that the startup Flyr seems to want to join in as well.
For Wideroe, this is true that they are largely serving small turboprop operations although there is also some overlap on routes also served alreday by DY & SK (eg: OSL-BOO).
Then you have Norwegian, Flyr and Norsk Atlantic. These all started with Norwegian, a Norwegian low-cost airline that eventually grew and had most of its activities outside Norway. When they pretty much crashed 1-2 years ago, the people behind Norwegian restarted the long-haul concept under the Norsk Atlantic brand. It is by no means certain that Norsk Atlantic will maintain any notable network out of Norway, from the sound of things they are aiming for a London Gatwick and Paris Orly hub again. I am not really familiar with Flyr, but my guess is they are also ex-Norwegian staff vying to take over the Scandinavian low-cost segment once held by Norwegian (which the new Norwegian is also gunning for).
That Norsk Atlantic are trying to do (long haul low cost) what Norwegian JUST gave up on is what baffles me likely the most.
One area Flyr seems to want to compete is from Norway to European sun holiday destinations. These routes are already served by Ryanair, Norwegian, SAS, TUI and an airline called Sunclass. So seems there will be a hyper level of competition on that market!
Wizz just shut the base at short notice. Didn't Ryanair shut its Norwegian bases in 2016?
True Ryanair nor Wizzair fly domestic but both still seem to fly from Oslo to quite a number of destinations around Europe but perhaps they don't have bases in Norway.