This is a good idea. I hope it gets traction (I'd love to work on this problem as well).
As for why some of this isn't done yet: The legal profession is old school. If you want to know where your work is, you can ask for a status memo, and you'll get billed for the time it takes to write it. Or the phone call. Either way. In industries where the product is the billable hour, you'll find things get done the way they've always been done.
You'll find small and mid size firms using more technology, but you'll also find that the more highly a company thinks of itself, the more it thinks it needs a large firm (which will bring its legacy processes, because they do work, even if not entirely efficient). Nobody gets fired for hiring Skadden, but then you also don't get to bitch when they do things the way they have for the last 50 years either. They didn't bring in $2.5B last year by accident - they're effective, and are going to be averse to process change if it risks outcomes.
If you're working on tech in this space, you also need to be aware of that. It's a tough sell to larger firms. They won't sacrifice outcomes or billables because it's all working really well for them, and they always have a glut of un/underemployed contract attorneys if they just need to throw highly educated bodies at a problem.
Lowering prices on mid-top tier legal work won't attract more customers, demand is largely inelastic. And their customers, who are fortune X00 types, don't really care about the cost. Oh, sure, they bitch and moan about bills and write op eds about how law firms are terrible and the billable hour is bad. But, in the end, like OP says, companies routinely go back to the same crop of biglaw firms. There is no such thing as 'disruption' in this industry, it never has been disrupted.
The only disruption that occurred was 2008-2011 or so, when the economy tanked and demand for legal services took a fall. Except most biglaw partners realized their labor model could change without consequence - they laid off tons of associates and when the demand came back, they replaced them with contract attorneys, paralegals, some offshore, some software and a small number of actual associate attorneys. It turns out what their 1st and 2nd year associates were doing was largely replaceable at a much lower cost.
That's the opportunity - but it's really hard when instead of software they can go get an actual living, breathing attorney to work on contract for $25-35 an hour. More in California because of their OT laws, so maybe that's where the opportunity exists initially for disruption.
Critically, though, I don't think anyone's figured out how to charge billable hours for what your software does. Since you can still bill contract attorneys out at 3x what you pay them, it's tough going.
In many other industries, yes. In law, not as much as you'd think.
Big law firms aren't really looking for efficiency. They charge for every 10th minute that they're doing something. If they have more work than they can handle, they'll hire more associates at lockstep salaries based on their "year" - or contract attorneys at less than half that if they only need some spare capacity to do rote tasks. Their labor costs are known and very stable, and with the sheer number of underemployed lawyers out there, it's going to stay that way.
No matter what, they're billing those associates or contract attorneys at far more than they're paying them. And the kicker is, the culture of "prestige" in the industry will basically prevent the largest firms from ever marketing that they'll do the same work in fewer hours. They don't pitch on a lower bill than their competitors, they pitch on expertise in a given area of law and a favorable track record of outcomes from similarly sized/situated clients. And because of that, few GCs want to take a chance on a firm doing things differently.
I'm not saying there isn't a place for Atrium - I'm not saying it's a hard sell to be negative. I really want them to succeed. It's just more likely to be in the small and mids where their clients do apply more pricing pressure, and maybe eventually in the larger firms if it really catches on. I think there's also an in-house play, because in-house counsel is often stretched pretty thin and needs better tooling to manage internal workloads and its supervision of outside counsel.
As for why some of this isn't done yet: The legal profession is old school. If you want to know where your work is, you can ask for a status memo, and you'll get billed for the time it takes to write it. Or the phone call. Either way. In industries where the product is the billable hour, you'll find things get done the way they've always been done.
You'll find small and mid size firms using more technology, but you'll also find that the more highly a company thinks of itself, the more it thinks it needs a large firm (which will bring its legacy processes, because they do work, even if not entirely efficient). Nobody gets fired for hiring Skadden, but then you also don't get to bitch when they do things the way they have for the last 50 years either. They didn't bring in $2.5B last year by accident - they're effective, and are going to be averse to process change if it risks outcomes.
If you're working on tech in this space, you also need to be aware of that. It's a tough sell to larger firms. They won't sacrifice outcomes or billables because it's all working really well for them, and they always have a glut of un/underemployed contract attorneys if they just need to throw highly educated bodies at a problem.