The main advantage is that it gives you an extra water bottle. Being lower down means that if you are swinging the bike from side to side it has less effect - this isn't about the 1kg being part of the total 100kg rolling mass, it's 1kg on a 10kg bike when you're out of the saddle on a climb.
Tourists often spend considerable effort on carrying water, because very now and then they ride somewhere with limited water availability (I live in Australia, that problem is more common here than in many other places). When your bike is already loaded for the rest of the tour, being able to add an extra bottle or two on the frame rather than balanced on top of the rear panniers is very helpful.
The same applies to longer road training rides, but I suspect it's a less common issue. When I did longer rides in NZ and water was plentiful, I still often used the extra cage to free up another cage for a toolkit.
That location also doesn't interfere with frame bags or shoulder carrying the bike. If you're bikepacking or touring offroad that can be useful.
This also works for bikes that have rear suspension and the frame doesn't allow a seat tube mounted bidon. Or for that matter, if you have a low top tube or a small frame that has the same restriction. In both cases this will be your second and probably final bidon.
Note that there are a lot of possible mounting positions, this diagram has the ones I've seen people use (I don't recall seeing anyone use all of them on the same bike, though):
I've also seen front fork mounts, and mounts for 1.5 litre or 2 litre soft drink bottles.
That bottom cage is right in the path of muck from the front wheel, so it will get filthy if the road is damp, and even in dry conditions the top fills with dust and gunk. On anything over an hour I find covering the top with a plastic bag helps keep the bottle usable. It's hard to access while riding, so that doesn't really hurt.
Note that this is normally the fifth or sixth bottle position on a bike, but it's often the third and final set of bidons. Why touring bikes don't have bidons on the top tube escapes me (my DIY bikes do), and with longer wheelbase bikes a set behind the seat tube is often useful as well.