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Depends of which part of the word WarGame gets the prevalence.

If we emphasis the "Game" part, something around 80-90%.

If its the "War" part, giving the randomness of a real battle, it is not rare to have the most competent general loose a battle because of exterior causes, so maybe 60-70%.

A very tight ruleset can be fair, but real life never is, so I guess it all depends if you are the "game as a sport/chess" type or "game as a simulation/narrative engine".

Voss wrote:

The thing is this kind of system presents a logical series of choices and actions which can result in that win. A new player can observe those, can be taught what to look for and can improve their game in logical steps toward improving their performance. They can learn, improve and develop

But they'll still be behind the more 'skilled' player, and therefore keep consistently losing, unless for some reason the 'skilled' player isn't also learning and improving. What's being presented here as a good thing is a closed system were veterans always win, and newbies are just victims until even newer folk join in (which if they're sensible they never will)..

You're still making the same mistake several are, which is to make the assumption that newbies will only ever play experienced people. You're also making the assumption that skill is like experience in a computer game and that if two people play the same number of games they will retain the same skill divide between them. In reality this is rarely the case. Often as not the experienced person will reach a capping point and the newer person will advance their game faster if they are given the proper support and education along the way.
Furthermore in any general club there will be a spectrum of player types. So you don't have to play the best in the club every single time. Furthermore there are means by which you can handicap the experienced person.

Also consider any other hobby - almost any hobby has a period of time where a new person is utterly rubbish. They will be worse than everyone else who has been doing it for a while and that is perfectly and utterly normal. Yes an increased amount of success in the early stages helps keep them around, but at the same time they've still got to learn. Plus don't forget there's building and painting which can easily take up hour upon hour of their time and be part of the hobby too. It's not just about winning/losing

IF at any point you can randomly lose because of the dice then that can be quite a bitter experience because now the dice hold sway

I haven't seen anyone postulate that any single moment causes random loss. That's a completely different argument.
When people complain about the 'dice' losing games for them, they're generally talking about long streaks of poor dice rolls- usually engaging in weird superstitions about dice, confirmation bias, or are making excuses for poor decisions.
The last time I saw people complaining about a die roll winning or losing games was back when random game lengths were a thing and someone did or didn't get an extra turn were they would have just 'wrecked face' and turned the whole thing around.