20+20+5=45, this doesn't make sense that by the character using a shield the mob almost doubles their damage. Which seems unreasonably punitive to shield users.
You are right that the math isn't mathing. But that is because it isn't supposed to math properly that way.
The game logic reasoning is more that the shield needs to be a limited resource that can be used judiciously during a fight, and that the benefit is both on-par with other defensive options and isn't so good that it becomes a must-pick.
If the shield negated 5 damage with its hardness, and then also absorbed 10 damage of the remaining 20 damage from the hit, then that is a total of 15 points of damage reduction on a 25 point damage roll. That seriously outclasses any other defensive option available in the game (Champion reaction, Amulet Thaumaturge, even spells like Mountain Resilience (Stoneskin) are only reducing damage by 20 at Rank 10).
And it only gets worse as you level up. At level 16, a Steel Shield with a Reinforcing Rune (Major) has hardness 10 and 104 HP. A level 16 creature with an Extreme rating Strike damage is dealing an average of 48 damage. So if the shield negates 10 of that, and then absorbs 19 more, that is almost a DR 30 item.
Having must-pick items in the game is bad for the character ecology. If shields can create that much damage reduction, then many characters are going to pick up shields to significantly reduce the threat level of the fights. And then the GM will have to increase the damage output of the enemies in order to be able to actually challenge the characters again and create some dramatic tension in the story. Which leaves those characters that don't have shields in a bad place where they are getting dropped in one hit. Which will cause even more characters to pick up shields. It becomes an arms-race cycle where pretty soon every character has to have a shield to survive even if they have to spend Feats to be able to use Shield Block or switch out their 2-hand weapons for 1-handed ones.
Shields also can't be unlimited use. Even with their action cost to use, they are still one of the best defensive options available. Making it so that the shield reduces damage by its hardness, but then takes no damage itself (the character takes all of the remaining damage alone), would not be as overpowering as having the shield split the damage with the character. But it would still make characters with a shield a lot harder to drop than characters without one.
As a curiosity from history, the first design iteration on shields didn't have hit points. They reduced damage by their hardness, but then had an even more abstract measurement to keep track of their finite resource - Dents. A shield had 0 Dents when fully repaired and would take 1 Dent each time it was used for shield block (I think it would take 2 Dents on a crit). When it got to 3 Dents, it could no longer be used for Shield Block.
People were outraged that items didn't have hit points, so it was changed. And the game has been the worse for it since. We still get questions from people about how to damage unattended objects or whether it is a good idea to allow Strike to target an enemy's worn armor.
Your shield prevents you from taking an amount of damage up to the shield’s Hardness. You and the shield each take any remaining damage, possibly breaking or destroying the shield.
As you can see above, Shield Block only "prevents YOU from taking damage equal to its hardness." This language clearly negates your first scenario. If the shield is taking all the remaining damage after the hardness then this sentence doesn't make sense.
The second sentence lays out what happens with the unprevented damage. "You and the shield EACH take the remaining damage..." "Each" shows that both you and the shield both take the damage.
As Finoan pointed out, this is because shield block would otherwise be overpowered as a defensive option.
It is not so much 20+20+5=45
it is more
25 dmg - 5 block = 20 dmg
apply final damage to shield *and* character
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Could anyone please clarify?
I had been saving shield block to stop massive crits and stay alive, or should it be used on smaller hits to use the hardness? My concern then is that it eats reactions that could be used for other
Yeah, using Shield Block on smaller hits works better. It's maybe a bit weird, but maybe not *that* weird.
The really, really big hit? Well you're hosed no matter what. You can try to put the shield up if it'll keep you above 0HP, but otherwise, it's a bit late.
The real profit is in using the shield against all the small hits. Instead of all the small hits grinding you down, you can use the shield to reduce them significantly (if you've been keeping your shield upgraded..)
It *is* a choice of how you spend your reactions. A reaction spent on the shield might be one you then don't have to do a Reactive Strike or for a champion reaction. Sometimes it's easy to see which way to spend your reactions is the best choice, sometimes it's harder to see. But that's part of the game: giving you choices that are not sooo obvious that they're not really choices anymore :P
From what I've seen in games, it can be a good tactic to really go for the shield. If right now you're getting hit and can use the shield well, and you don't really know if the enemy is going to trigger a reactive strike, then it can be solid to just go with the shield instead of holding out for "maybe I get to Reactive Strike". If enemies are focusing on attacking you but you can negate a lot of that, that buys time for the rest of the party. It's really a choice between "is my job to hit the most of everyone" or "is my job to hit, but also to buy time for other people to hit".