But of all the variables, wonders "hurt" you the least. The increase is the smallest. Unlocking mandatory techs is the biggest ouchie factor for most people.
Essentially the ratio of troops is preset for everyone at the same point in the Spire and Tourney province. Things like wonders and unlocking mandatory techs increase stack size brought to battle and cost of catering. Increase in stack size results in more dead troops so you have to be able to replenish your stocks in time, week to week. You counter this with things like upgrading your barracks, merc camp, and training ground. However, most chapters only allow you to upgrade one of these buildings (some chapters 2). You can further offset the troop increase from the formula by upgrading military wonders that increase production speed (Needles, Flying Academy, Victory Springs). What happens in late chapter is you will reach a point where the troop increase from unlocking techs will outstrip the rate that you can make them by upgrading your military buildings from techs.
There are also military wonders that buff up your troop's ability to fight (Heroes Forge, Dragon Abbey, Victory Springs, Needles, Toads). If they are stronger, it helps them win the fight in less rounds (you can see this effect manual fighting), which can help save you troops as well since they don't have to take more rounds of beatings. Now if the ratio is preset, it means you go to battle against the same ratio but with more buffing. For example (making up numbers), without wonder upgrades at a certain encounter, it might be 100 vs 300. After unlocking some techs and upgrading wonders, you might see 200 vs 600. Hence, you're still fighting 1:3 ratio, but now with maybe 5% buffing. Then the question is, well is a small increase to say 6% buffing with size increase to 300 vs 900 adequate or worthwhile? If you manage to max it out, I think you get a 40% buff though. Paired with a fed Fire Phoenix, that's a significant advantage.