We can't patrol or garrison the entirety of the river, and there's literally nothing stopping them from crossing over the part of the river beyond our frontier. It's a good goal, but massively expanding the front along the entirety of the known Black River is fucking insane as things stand. There's a reason the only major civilization that conquered the steppes from the steppe nomads was Russia. And we don't have anywhere near the conditions to do the same until at least iron working. You're asking for us to strain our logistics, hold an area far larger than the rest of our polity just because it has a somewhat defensible border? That's the only point in it's favor.
Furthermore, the nomads will always be raiding and always be a threat. Once we actually secure and conquer the Lowlands, it's going to be a hell of a lot easier to protect and hold that land than it is steppe that's nowhere near as productive. The fact it eventually brings us into conflict with the HK is immaterial.
You're asking us to go invade the lowlands, which will have no better defensible border than a river and will strain our logistics in an identical way.
I think that we can watchtower the entirety of the river, especially any notable fords, and that the river's existence will serve as a barrier regardless. It is not larger than the rest of our polity, or at least what I am advocating for - expanding up to the river so we make a triangle, as veekie suggested earlier - is not. Taking over the whole river valley might be, however.
AN said that the lowlands we have been to have the same soil quality as our provinces in the north. A conflict with the HK is extremely material, as it's a whole other group that we'll be going to war with. It will bring us into conflict immediately, as your goal is literally the same as theirs: attract lowland groups into our political sphere and develop their land.
Your plan is either that a) we will mysteriously conquer all of the lowlands and thus not have to deal with anyone or b) that we conquer a small part. If b, we will still have to deal with raids from the TS & TH and, at this point, probably from the XS and HK too. Nomads will be raiding in the north regardless, so them continuing to raid isn't much of a change except that now we're actually doing something -i.e. expanding into their land which, again, is as good as the lowland land you propose that we conquer. Meanwhile, the southern border can be made increasingly secure because we're not already extended into that area to as significant a degree as we are in the north. We only have Redhill down there; in the north we have ST, Stonepen, Northshore, and Blackmouth.