Why weren't these barbarians a threat in the 4th century?
Mostly because Romania was in better shape : in spite of the succession crisis (that weren't as anarchic as it happened in the Vth century among other reasons because they were largely built over a dynastic principle), institutions remained strong enough to be maintained. But eventually, even this grew thin as ressources couldn't be gathered as quickly that they were needed.
The managment of the empire more and more weighted on imperial structures (the emperor himself of course, but also his court, his direct subordinates, his court administration*), and the political crises of the late IVth didn't helped.
Furthermore, you didn't have as much pressure on borders after the crisis of the IIIrd century : it really began to be a problem by the late IVth century (when Hunnic hegemony pushed groups westwards), and didn't really stop until Romania couldn't efficiently hold of all of it, then any of it.
So, roughly : Romania in the IVth century could deal with its issues for a while, until the whole structure became weary by the Vth. It was salvagable, but there were payed the missed time of the second half of IVth century.
*Let's remember, tough, that Roman Empire administration was still both a bit of a mess, and a limited structure : it never reached the ratio it did in ancient China.
What if the Crossing still happens, but they join up with an Emperor of Rome, as many did for Constantine III?
It's basically what many Barbarians actually wanted : the prospect of serving the Roman State, especially within the army was both a prestigious and rentible opportunity for most of them.
The problem being, they were not going to ask that politely and in order : or more basically, they were not going to cease being Barbarians with a distinct popular/political identity even if Roman nobility would have accepted that.
Of course, you had as well the usual band of raiders or adventurers searching for diverse opportunities (think conquistadors, with less motivation on actually conquering anything, as Radagast in 406)
To further complicate things, as you said, you had generals and officials of Barbarian origin serving Rome in the late IVth/early Vth as Stilico or the whole bunch of related Frankish-Roman generals and masters of militias : Ricomer, Merobaud, Nebiogast, Arbogast, Bauto...
Even if it's maybe a bit too simplyfing : Barbarians wanted to serve the Empire (not exactly out of idealism, but because it was prestigious and promising when it came to gains), met with many usurpers that allowed to do just that or dwelled in Romania (mixing up with foederati, laeti or Romans) as armed groups generally do when not engaged (basically doing what routiers did in Middle-Ages, except they had a relatively more important political cohesion).
On that potential PoD -- listening to the old podcasts by Mike Duncan on this period; according to him, Stilchio didn't really respond to the Crossing until the spring of 407, likely due to him not having very good information.
Misinforation can have played, but I'm not sure it was the determining factor : look at WRE in 407 and put yourself in the shoes of Stilico for an handful of seconds.
The weak point of WRE was so far Danubian borders
-401-402 : Vandals attack Raetia
-401-402 : Alaric raids Illyricum and Northern Italy
-405-406 : Radagast raid the hell out of northern Illyricum and Italy
Furthermore the recent revolts in ERE could make Stilico think he won't recieve as much reinforcement that he could expect normally : hence why he resorted importantly to Hunnic mercenaries.
Could a better information or assessment on the Rhine help? Maybe, but not immediatly : for all Stilico could see, Danubian regions were the soft underbelly of Romania, where most of the trouble makers were so far.
I'd even think that if Stilico didn't took troops from Gauls the previous years, it wouldn't have really mattered : it seems as Barbarians actually had good intelligence at this point, going for the soft point in Rhinish limes and directly going against the Frankish foedus that served as an important border army for Romans (maybe as well to make a point about how they felt Franks monopolized a bit too much imperial favour).
What could Stilico do? Send back in emergency the troops that he took from Gaul?
That's admittedly possible, but would have come with a cost : Stilico's power depended a lot from imperial favour and actual results. Showing weakness could have turned badly for him (his fate points how much such a fear wasn't exactly paranoid).
Now would have he done so, what would have happened? It may not even have prevented Constantine's usurpation, wouldn't have embettered Rhine defense (it seems that IOTL, the limes was quicly reoccupied) and would have weakened Danubian border : congratulations, you just made Alaric (who didn't recieved the money promised so far) a threat one year earlier than IOTL.
So, I agree, a bitter intel could have been an asset : but how much would it have impacted on the quite difficult strategical decisions that Stilico had to take?
And while the question of Stilchio falling from power sooner or later is debatable, I think we can all agree that keeping the asshole who overthrew him OTL, Olympius, from coming to power can only be a good thing.
I wholeheartedly agree : while
maybe not as cartoonishly incompetent as how he acted during his mandate, he was certainly not fit for the role, for the situation...for anything that didn't put him in a subordinate role.
Not that killing Stilico was that problematic (even if it was, the assassination was made far too late that he could be replaced efficiently) : he was actually too engulfed into court politics to not being considered as a threat by part the imperial court. But he should have been replaced earlier in this case, and by someone actually competent in the position of commander-in-chief.
Maybe Constantine III does better in 407 (or early 408),
With the few troops he had, I'm not sure that would be doable, at least in a significant way. Maybe if Frankish foederati do better in 406 (for exemple, Respendial doesn't manage to help Godigisel dies and Vandals defeated), while it wouldn't stop the Crossing at the latest, it could provice Constantine with a few more men, and maybe limit a bit the damages.
But really, I don't think that much could have been done at this point to stop the Crossing or the Barbarian advance afterwards : Marcus and Gratian didn't managed to find a way to do so (and it's why they were killed-replaced by Constantine).
The behaviour of western Roman army (made up of both Romans and Romano-Barbarians at this point) let little strategical possibilities to Constantine (maybe even less than Stilico).
Maybe, if Stilico is killed early ITTL, you could see Constantine being acknowledged as co-emperor earlier as well. It might help a bit (and may butterfly away its IOTL dead, making him able to weigh more in 410.
More importantly, it could lead Constantine to have more men in 409, when the second big wave of raiders and crossing people came in Gaul. Again, don't expect him to blockade them : he's there to limit damages.
But don't focuses on 410 sack : it have almost no strategical value, and almost no consequencie on the fall or survival of WRE. Honorius was spot on this : better being raided a bit too much than loose political legitimacy and coherence.
As soon as Honorius was dead IOTL and was succeeded by a military anarchy, backed as a ping-pong match between Romano-Barbarians and Constantinople, WRE was effectivly agonizing.
Repeat : don't focus on 410, but rather on giving as much strength to Theodosian dynasty. The usefulness of Constantine in this scenario isn't about winning symbolical battles, but to hold more ressources and military for the empire. If he dies, he dies and get replaced by someone else.