Again, with the exception of Sanctuary/Martial Monastery, if they're just playing a few provinces in the tournaments to hit a minimum of 600 or 1000 points, for example, will they really feel the effects of tournament-specific AWs?
There aren't actually any tournament specific wonders other than Time Warp since you can fight on the world map too, but yeah, building a powerful military for just the map would be very wasteful.
The more AWs you have the more space you have to forgo that could be used for other buildings. You could argue that once the AWs are high enough levels they will pay for the space sacrifice and more but that's going to take you longer the more AWs you have to level.
There are several wonders that "pay for themselves" space-wise at level 1
- EE, PT, ToS. Each of them are better than workshops at level 1(with extremely rare exceptions like making bread 24/7, cycling quests like a robot, only collecting from PT once a day, and 72H+ scout times)
- Shrewdly shrooms- this building is an absolute must-have if you want to use military. Even at level 1 it's better than a third armory, and it takes up zero pop.
- Dwarven bulwark-generally KP invested in the shrewdly is better than the dwarven bulwark, but you might unlock the bulwark months earlier which makes this a great wonder until then, and if you level it, it's not worth deleting.
- Mountain halls- any build that has at least 6 factories is better off building a MThall than building a 7th factory. The more factories the better it is, and that's not even counting the pop it gives you.
- Golden abyss-once this gives better pop per square than a house (around chapter 5/6) it's an obvious win.
So right there are 5 wonders
space saving wonders that basically everyone should have and another 2 that most players should have.
The more AWs you have the greater the list of benefits you will receive, granted, but the size of those benefits will be smaller than if you only concentrated on select AWs. You'd end up with smatterings of different benefits, which will take you longer to feel the effects of.
Let's take the case of a player with moderate to high level of tournament activity:
First the military damage wonders:
For an investment of 6,200 KP, they could have:
Needles level 18 for +26% Light range damage
or
Needles Level 6 for +12% LR damage, and
Abbey Level 6 for +12% mage damage, and
Heroes Level 6 for +12% HR damage, and
Victory Level 6 for +12% HR damage, and
Toads Level 6 for +12% HR damage, and
Monastery Level 6 for +9% health all units
So 26% damage in pretty much just the steel tournaments, or 12% more damage and 9% more health all the time with every unit.
Then we look at the other benefits
Needles Level 6 vs 18 is a change from 130% training speed to 165%, so 27% more troops trained assuming you only use the barracks and run it 24/7(at an increase in supplies cost of 27%)
or
Needles Level 6 30% increased training speed, and
Abbey Level 6 for some mana per spell cast, and
Heroes Level 6 for free orcs, and
Victory Level 6 for faster training grounds, and
Toads Level 6 for free HM units, and
Monastery Level 6 for +12% culture
Is it worth the extra ~5 expansions? For the player with moderate to high level of tournament activity, I believe so. Having a more well-rounded military should equate to getting far more KP from the tournament each 9-week cycle which can be used on the 7 space-saving wonders listed above to easily make up those expansions.
Which leads onto strategy and playing style. ....... If you're not a tournament player why build tournament-specific AWs at all
A pacifist player (tournament or not) should probably just build the 5 core space savers and ignore all others including the culture ones and make use of hybrid event buildings so that they don't need any.
If you're a tournament-focused player why not concentrate on tournament-specific AWs?
Yes, other than the 5 core space savers, concentrating on military wonders makes the most sense for a tournament focused player.
And then you have players who play purely for the visual aesthetics
I'm fairly certain that I've seen every wonder called ugly and pretty, so I usually don't even address this subject