They said it a few chapters back, they are a church nation, that is currently divided in two factions. It was framed not as a general church, but more as that nations ruling party.
This makes me doubt their influence is as powerful as say the catholic church. And if they are split in two, then it doesn't really matter how large the churches influence is as they are at least semi in balance with the other faction. So in doing this they will add the guild as a enemy and a ally to the other faction.
Now in worlds with a guild it is generally a very large powerhouse, often one of the largest. It does depend on if its international or not, but in general adventurer guilds are even more untouchable than a nobles, or churches. The reason being that they control basically all the mercenaries, are international and can pull out of any nation that bugs them, as really the guild doesn't need any of the nations, it just manages the adventures who manage the monsters. Do to this adventurer guilds tend to be very influential in most stories.
That said yes they could be a lot less, but even if they only a small power, the entire point I am making is, they are making a enemy, for nothing. The knights can just say they failed, remember they work for the faction that wanted this "saint" dead. They just say they failed, and their faction will cover for them and keep them employed as this "failure" was them succeeding. They can just hide the names of the knights who were on the mission, claim it was something out of their control.
They have no need for a scapegoat. When they will be the faction in power. So they gain nothing, and it adds a enemy, one with a info network, and ability to spread information, they lose control of the narrative for nothing here.
I honestly don't think we'll ever agree on this.
I saw them refer to "the Holy Land", which is an ambiguous term. While it could refer to a nation (especially with the lazy naming conventions you can get in manga), it could also
easily refer to a region. Perhaps even within the kingdom itself, or a Vatican/Italy type setup. I also saw no indication that it's a single nation church, everything seemed to me that it's more widespread than that.
I've read plenty of isekai and fantasy manga where the Adventurers Guild has huge power and influence over the whole continent or world.
I've also read plenty where the Guilds power and influence is
much less, from an important national organisation, to a loose alliance of individual city and town based guilds, all the way down to being basically relatively weak and disliked place to hire ruffians and wanderers for crappy dangerous jobs that no one else wants. I've seen them were the adventurers are basicaly the Guilds private army. I've seen the opposite where the Guild is just the place where a whole bunch of indipendent adventurers go to get jobs.
My point has been
we don't know what the Adventurers Guild in this setting is like, and I've seen no real evidence either way (other than it not being on the really weak end of the scale). If I had to hazard a guess, it'd say moderately important on a national scale, with nothing (yet) showing it to be on the powerful and influencial "don't fuck with us" end of things.
That last point, the one that is "the entire point" you're making, is the one I have the most issue with. You keep harping on about they're 'making an enemy for nothing' and 'they don't need a scapegoat' etc. Really?! A Very Important Person dies and their escorts can get away with just saying "Oops LOL!" and that's it? You say 'their faction just covers for them'. Guess what helps with that? A SCAPEGOAT! Bonus points if they get a confession (through torture, magic, forged written confessoin, whatever).
Unless the other faction(s) are really stupid, I doubt they would just accept the equivalent of 'she died somehow' or 'the killer escaped'. That's the kind of thing that is more likely to lead to their own investigations, or more thorough investigations than they otherwise would. And unless it's covered up really well (admitedly possible), they'll need someone to blame for the general public. Both for the general public to aim their anger at (for killing the beloved Saintess etc), and to make the Church seem less of a failure (oh no! we were too slow to save the Saintess
fake tears but we at least caught one of her killers! see? we're not useless, justice will be served!
perfomative theatre to control the masses).
As for the 'enemy for nothing' bit, we don't know what their goals are. Maybe they WANT to ferment hostility between groups, maybe the secretary was an unexpected (minor) wrinkle in the plan but they're going for it anyway. Maybe the see--rightly or wrongly--the guild as too weak to realy do anything. Maybe they expect the Kingdom will make the Guild accept the verdict. The Saintess died in Kingdom lands while being escorted by a Kingdom adventurer after all. The church could very well demand reparations or something. The 'kill the saintess' faction could easily have allies within the Kingdom's nobility, close to the King, inside the Guild etc.
Why did Cardinal Whatsit want an adventurer to help with the escort? To get a convenient scapegoat with no real power backing them. Makes covering for the real culprits much easier.
That is, unless he arrested the secretary as a cliffhanger fake-out and he's not actually scapegoating anyone, making most of this debate kind of irrelevant. I mean, he
could be 'arresting' her in some kind of effort to protect her and/or draw out the real culprits or something.