Being able to send more troops appears to give the advantage of being able to lose more troops against larger enemy squad sizes.
This true, although Squad Size was removed from Spire/Tourney calculations in Oct 2020 so Squad Size techs mostly only affects map provinces, unless they were a mandatory tech in the tech tree. Map provinces have more to do with scouting. For example, I am under-scouted so all my map provinces are "Very Easy". I can pretty much close my eyes and randomly select any 5 units and walk away with a win. If I take it more seriously and select units properly, then I can almost do them without much of a scratch since, for the most part, your units go before the enemies and if the province is "Very Easy", you can kill them in one shot. If you sneeze, the enemy will fall over and die.
The way I understand it is that you only lose more troops when you lose the whole battle.
Oh, it will hurt in the upper provinces for sure, even without even losing the whole battle. For example, Mist Walkers go before everyone, whether you are playing a human or an elf. In the upper provinces, the enemy stacks could be 2x+ your stack size. So one freebie shot out of her will hurt a lot! In the last Planks tourney, there was one upper encounter where I faced 3 Mist Walkers. I watched helplessly as they destroyed almost 2 full stacks before I am even allowed to move. Had to fight it down a man and another stack barely hobbling.