You can't compare approval of companions, Geralt doesn't have any. It is significant to DAI, but wouldn't be to TW3 or any other rpg that doesn't have companions. Also, I wouldn't necessarily say that your personality or character agency has anything to do with the epilogue as much as just choices you make. For instance, if I start the game off hating mages, then have a change if of heart and save them as allies, the epilogue will be the same if I loved mages to begin with and recruited them as allies. It was the choice you made that checked that plot flag, not how the Inquisitor changed their mind.
I HAVE to compare the approval of companions, considering that they're such an integral part of the game - casting them away is simply out of question. This is where both games differ significantly - Geralt has no stable of constant companions, which is why he has world that is (has to be?) more intractable. DA on the other hand focuses on companions/specific NPCs and a lot of our decisions is reflected with how they treat us or how they end up to be, which is why either many side-quest are underdeveloped - or at least they feel that way for some people.
Also - when it comes to your example with mages... how you treat mages will be reflected with how your companions treat you. If you don't coddle rebel mages and conscript them instead of trating them as allies, you'll loose a lot of approval from Dorian and Solas, but gain it from Vivienne and Sera (and Cassandra, to an extent. Leliana and Cullen will have different reactions as well).
This, eventually can also translate to who becomes the Divine - and how strong the friendship between Divine and Inqusition is strongly reflected in new Divine's course of action, which in turn decides A LOT about many plot elements (will Southern mages establish College of Enchanters or become members of Bright hand? Will Leliana urge unity through negotiations or knives and murder? Will Vivienne stay the first mage Divine with Inquisitor's support or will her end be imminent?)
They react in a cutscene and conversation only. After that, it's as if everyone forgets about it. You may lose approval points, but you can gain them back and nothing will have changed for your decision. Can't really count for anything that happens in the Keep. Not everyone uses it and it doesn't reflect anything in-game. Which is what I am talking about. You're right about the extra dialog if you are a faithful andrastian, but it's the same dialog you receive if your Inquisitor begins as an atheist and changes heart midway. No one remarks on how much you've changed or that they're glad or angry that you've had a change of heart.
They don't. Many decisions are also reflected through banter we hear when exploring the zones, so they definitely don't forget about anything.
As for losing and gaining approval points - the system is somewhat flexible, for which I'm glad. You still have to play smart to actually gain significant approval of all companions, - I don't feed them treats to gain their approval, I actually have to actively balance between things they like and they don't through entire gameplay. I really like it - makes me feel like a true diplomat
Someone who may not be bent on gaining max approval, but with being open-minded and smart enough, I at least gain everyone's respect.
You have to complete the watch towers, or else you'll have no horses and miss out on an agent--but if you refuse to do it, no one comments on how the Inquisition is ignoring their safety. You have to capture most keeps to progress the story along, so opening trade routes is automatic by doing those. If you don't gather food and clothes and a healer for the refugees, then you again, miss out on an agent, but if you don't do it, no one comments about how you're letting refugees go hungry or they're dying because you didn't secure them a healer.
Um... just like you have to complete many quests in Witcher that change people's attitude towards them? I'm not sure what point you're trying to make.
Add to that the fact that both horses and agents in Inquisition are entirely optional. You have to make an effort to actually get them. And no - opening trade routes isn't automatic, since you have to complete additional quests and war table mission to actually open them fully AND make them secure.
It's the same with Geralt - you actually have to do something for people to comment on him. If he doesn't, the most they do is they say "Witcher? Pfeh, I've seen more interesting things after rummaging in my nose" (or however else it's translated to English) or call him "Freak" for the 100-th time. Not really different to DAI in that respect. Both characters have to be proactive and do more than just main story quest to have many people talk about them.
Patrols and agents with chests will appear if you claimed a camp in the area, sometimes you have to clear out bandits to claim a camp and once I went to Redcliffe doing only the watch tower and ram food mission, iirc and people were still talking about joining the Inquisition and I hadn't done squat. So those things aren't reflective of the Inquisitors personality or the way you shape him, but more of things you have to do to gain something or progress the story along.
It's obvious that some people would want to join Inquisition even if they've done little, but more people will be commenting on Inquisition the more things you do.
Also - how does Inquisitor running Inquisition effectively, or by doing many things, doesn't reflect anything about their personality? People won' be singing peans about how good or cruel they are or anythings specific like that, but that's also because with how both characters are framed - Geralt is just one person, nobody really that important in a big, war-torn Continent.
He's a Witcher, true, and people will judge him accordingly or change their opinions depending on his actions, but they'd still be able to interact with him on more personal level than Inquisitor - a point that has been actually stated multiple times throughout DAI (how legendary figures are both more and less of a person at the same time).
Herald of Andraste won't be able to be so up close and personal with majority of common folk (or even someone higher that that), simply because for most folks he/she is either a demigod or someone of either immense importance or popularity. Hence what else they could be commenting on other than efforts of Inquisition?
Isn't it? When compared how your personality reflects the living world around you that isn't scripted because of a mission?
Like I said - agents, horses, gaining all of keeps and re-opening trade routes later: all of this is optional, which hardly makes those missions scripted. They're only 'scripted' in a sense that something has to be done, which is no different than TW3.
Disclaimer: I have the summer flu, so please excuse any grammatical or spelling errors
And I apologize if this comment is maybe a bot more unfocused than my previous one - it's very late (or, very early) where I live and I really should be going to sleep now^^;