Prior to the tourney changes in Oct 2020, activating those optional SS techs increased the cost of fighting and catering in the
tourneys. Since most players do way more tourney than world map encounters each week (esp back then when each round was 4 encounters), the general consensus was it was best for all players to skip those techs. That's because the
formula* for increased 'difficulty' was based on your regular SS and impacted both fighters and caterers. Province encounters were never impacted by SS and Spire encounters launched with a different formula that did not use SS. When the change was made to tourney structure in Oct 2020, the tourney formula was very similar if not identical to Spire encounters.
As a player who had skipped all optional SS, I went back and completed them for event quests. There was no reason
not to do so and it improved the output of military AW's that provide extra troops based on SS.
*formulas: please note that Inno does not release these formulas. The current Spire/tourney formulas were done by a brilliant mathematical mind that has since stopped playing: MinMax Gamer. He crowdsourced the necessary data and reverse engineered the formulas. He has thankfully left all the info available to us on his site
here. You may have to click around a bit to get to all of the info. I don't pretend to understand more than a tiny percentage of that info, lol! I was lucky enough to be here, participate in it, and follow along with the questions/answers in real time. Otherwise, I'd just have to take his word for it, lol! If interested, you can see the forum thread for Part 2 of the crowdsourcing effort
here. There is a link to the Part 1 thread at the top of the first post. They're long threads, but that's where I became comfortable that his info was as close to perfect as it could be. I can't find it right now, but there's a calculator from him where you input your Spire squad size in the first Spire encounter and it continues to track well with results, leading to my belief that the formula remains unchanged at this point.
@crackie Do you have a link to that calculator?