Well, it is not the *best* story but I perceive it to have much sense actually. So my understanding is (and some possible SPOILERS ahead):
1. Alec Ryder was N7 and creator of SAM. He was one of the main *developers* of Pathfinder role, of how it is expected to function, of related protocols, and possibly required background and training.
2. There is a saying in many military traditions that perfect decision too late is much worse than imperfect action on time. Andromeda Initiative was aware from the very beginning that they were running on limited resources and that there was no time to debate and discuss all pros and cons on every single decision. So they agreed that dedicated person with a lot of experience, and possibly some additional training in relevant protocols will be ultimately responsible for making *some* of the decisions (like which planets to settle, where, and when; how to approach alien civilizations; etc.) with no option for others to veto. Since there is still a lot to consider on the fly when assessing planets, circumstances, and situations, SAM was supposed to provide enough instant-time feedback and analysis so those decisions could be truly taken by one person in a sensible way.
3. Scott and Sara have military background, and are adequately educated, but are far from being N7-level. Thus Alec's second in command was Cora, who is an accomplished biotic commando with a lot of skill and experience. Perhaps not N7-level, but pretty close. Being a Harper could have played a role as well - we won't be sure until the sequel. So the idea was to have Alec as human Pathfinder, with Cora as his back-up.
4. [BIG SPOILERS] Alec was aware of Benefactor, and was suspicious about him or her or them. Perhaps he suspected Cora to be a part of Benefactor's plan to take over the expedition, and perhaps (though I doubt it) Cora was even supposed to kill Alec shortly after arriving to Andromeda. Immediately before Alec actually died, he considered his options: there were very few people he could have truly trust, and he had his own agenda with SAM, Scott, Sara, and his wife. So it was pretty obvious that he selected his own child rather than Cora to take over SAM.
5. So Scott or Sara was bound to SAM, which as per Initiative protocols made him or her a Pathfinder. Alec's child is the only person that can employ SAM to evaluate planets, locations, and life forms in microseconds, and thus take informed decisions where others would need to base on luck or instinct. As per in-game explanation, there is no real way to select another Pathfinder without killing Scott/Sara, and actually there is no such precedence anticipated in Initiative protocols. So Scott/Sara now *is* a Pathfinder, no matter how much or how few experience he/she has.
6. As far as Nexus is concerned, there is really no one to question the choice. "Administrators" can mock Alec's child and play their politics all the way, but they are too inconsistent and divided to make any actual moves. There are in-fights, accusations, and emotional issues, plus Tann, Addison, and Kandros are probably well aware themselves that they are not the best people to govern the whole Initiative. When Ryder arrives to Nexus, Initiative is on a verge of extinction, and its administrators are expecting further bloody protests / domestic strikes. What they are actually doing is using Ryder as a diversion, and possibly as a scape-goat. If Ryder actually helps, they will be able to tell their people that they supported the Pathfinder from the very beginning, and that Initiative was eventually successful. If things go sour, they are willing to say: "OK, so there was a Pathfinder expected to help us. We had not trusted him or her, but that was his or her job, so we cooperated. He or she failed, so we will now need to take over again, and perhaps we will manage to find some other solution". They are petty clerks that are unexpectedly governing, and they need to play high stakes, so they are playing high stakes. It is a political game, and it actually makes much sense.
7. [BIG SPOILERS] From Benefactor's point of view Alec's child is an unknown. Situation is far from what his/her/their faction expected, with Scourge, Ketts, no paradise worlds, etc... And young Ryder is supposedly unaware of the hidden influence, so *not yet* a liability - just "a hazard" at most. Perhaps it would be OK to let Scott/Sara to play Pathfinder for a time, to decipher Remnant codes, to keep people happy, to act friendly with aliens. Of course, it would still require keeping Ryder under surveillance, and remaining prepared to remove him/her from the equation if need be. But there is no such need *yet*.
8. In the meantime, young Ryder turns successful. There are outposts founded, contact with Angara is much friendlier than it could have been, Ketts are being dealt with. There is no good reason to replace him/her, especially since lives of all the involved parties possibly depend on those successes. At the same time, all the involved parties want to remain on top, and thus they cannot allow Ryder to become too cocky. They need to temper him or her, and to make it clear that Pathfinder works for the Initiative rather than the other way around. So there is a lot of those nasty emotional, psychological, and political games. We do not know if Ryder is aware of the fact, and just plays along in order to remain in the game; or if he/she just does not yet feel secure in the role, and thus had not yet grown a backbone. All the same, until enough influence is gained, Ryder cannot play too hard - or he/she will be immediately removed from her functions as "untrained", "unskilled", "done her job already". Even if current administrators are unable to completely strip Ryder of Pathfinder status, they can still make his/her life a struggle, and to dampen all his/her efforts.
9. So here we are: young Ryder is a Pathfinder, not because he/she is the right person to be a Pathfinder. Alec played his hand well, and then it occurred to be an "acceptable" (or even "convenient") solution for all the involved parties - at least for a while. Young Ryder has few options, and must play nice, at least until he/she gathers own resources and builds own alliances - which always takes time. It is imperfect situation, and imperfect decision, but it was made on time, and proved to be right in hindsight.
10. [BIG SPOILERS] And I really do hope that Ryder is planning ahead, since Benefactor will certainly wish to either "buy" Ryders in; or to kill all the Ryder family sooner rather than later...
