I restore and rebuild sashes. Occasionally we will get a job like you are talking about. Partially it depends on how deep down the rabbit hole of window sash building you want to go, and what the budget of the job is.
Two books that I found super helpful on the topic are The Window Sash Bible and Save America's Windows by John Leeke. If you want to do more work like this, they are probably worth reading. Especially the one by Leeke. Plus there are some affiliated forums on his site that can answer all sorts of questions like this if you use the search.
Those books will give some perspective on why things were built the way they were. There are quite a few advantages to traditional mortise and tenon construction that may or may not come into play on this particular job.
The first sash I ever built, I used a window sash bit set from Infinity Tools and I used a Domino for the joinery. It will definitely do the job. These sash in particular were fixed in place, so they weren't likely to be subject to some of the abuse a double hung window might be.
Also worth considering is repairability down the line. If you are trying to build something that could last well over a century with proper maintenance (and material selection), then the mortise and tenon method has some advantages. Basically you don't need to use glue if you get it right, and you can pin the sash square with a finish nail or a peg.
With a domino you are likely going to want to use some waterproof adhesive, which usually means epoxy though I would not be surprised to hear of people using other products. But once you seal a joint with epoxy, there's not exactly a clear path -- certainly not an easy one -- for the guy who might be tasked with maintaining the sash down the road. Then again, if you use a domino and some epoxy, the joint will probably last at least 50 years (from what research I have done), and would probably be less likely to go out of square.
The gist of it is, if you start getting into doing sash work, you're going to have to become super proficient in all manner of mortise-and-tenon joinery. Mortise machines, router jigs, hand chisels, rasps, and yes even the Domino will all be necessary tools for different repairs, or at least they are for me.
So, at that point, if you've got the time and the kids aren't starving (or existant), it's probably not a bad way to learn how the old-timers did it. One benefit I haven't talked about is that if you use a through mortise, the end grain will 'poke through' the vertical sides of the sash (stiles). This will allow the wood to breathe / dry out, which could give it a fighting chance if the maintenance is not kept up with.
If you want a good hybrid approach that will get the job done quickly without needing too much tooling, you could use a domino to make the mortise (I purchased a proper 3/8 bit from Seneca Woodworking for this, but 10mm is very close), and then make the tenons on the Table Saw (or whatever you want, that's just what I use). So there wouldn't be a loose tenon, but the most time consuming part of the operation -- and the trickiest part if you aren't used to using hand tools -- is getting that mortise dialed in. So the domino would save quite a bit of time there, potentially. I've seen videos of guys like Paul Sellers doing very accurate mortises in almost no time at all. They make it look easy. Depending on how much material you want to waste and where your skills are at now, this may or may not be the project to learn on.
Hope that rant was at least peppered with some relevant info. Let me know if you have any more questions. Not sure if they are on this forum, but there are some other websites where some very proficient -- like, leagues above me -- sashmakers dwell. They can occasionally be roused from their dark lairs. But from what I know of those guys, they are probably not using festools. Many of the best tools for sashmaking -- machines, really -- were made in the 1920's and before, I believe.
Essentially there are two camps. Guys kind of winging it in their garage and guys who hunt down the old machines that were designed to churn out huge numbers of sash efficiently. Pretty much everyone starts as the former, and some chosen few follow the shaving-laden path toward the latter.