The overall risk comparison between being alone or in a group can be split into parts:
falling: no increased risk
This is obviously independent of being in a group or soloing as climbing on a via ferrata is a solo activity.
severity of fall: hardly any increased risk
The safety device used on via ferratas is a single user device. So the only factor contributing to a more severe fall would be a handling fault. The risk of this could be decreased by partner check in a group. However the initial setup is so easy that there is hardly room for mistake. And while climbing the major misuse is being completely detached while changing from one section of steel rope to another. This error is very unlikely to not be spotted by yourself (after all one arm will hang down).
rescue: potential for much more risk when alone
This is the main benefit of being a group. A via ferrata is a no fall zone, as a fall will most likely have big consequences. You are stopped rather harshly (even with modern dampers this is far from smooth) and there are lots of metal rods, wires, ... sticking out of the rock to injure you. So it is very likely that you will not be able to get off the via ferrata on your own. In this case it depends a lot on whether there is a rescue service i.e. how fast it can be on place and whether you have means to contact it. However there is also a chance that you hit your head and lose consciousness. In this case you are in high risk of suspension trauma which is potentially deadly (all depends on how fast you regain consciousness).
So in the end it is the usual case where our ability to asses risk is not very good: You have an event that is highly unlikely (you don't fall on via ferratas, slipping with both hands and feet is highly unlikely and you can always rest) on the other hand the outcome of this event is potentially disastrous. It is a personal choice and there are these mentioned factors that make it somewhat less risky:
Regarding your last question: Well frequented is nice and it helps somewhat if there are other climbers on the via ferrata, but you cannot know in advance whether there are actually people there when you want to go. And even if there are people: If they are far away they might not notice you falling or they might take too long to reach you (suspension trauma), in which case they could at least get rescue (if contactable).
A colleague of mine does this for training as you intend, but he does not take a via ferrata set, so he is actually soloing. While I obviously cannot encourage anybody to do this, it is consequent. In my opinion (so this is by no means objective!) if you aren't able to accept that a fall is fatal and still go, your (perceived) risk of falling is too high to go on your own.
Falling on via ferratas (properly secured) is dangerous and it happens, even if seldom. So I cannot recommend going alone, certainly not if you have to ask online whether you should go or not.
One very important thing that I completely missed: Ascent to and descent from the route. These may just be perfectly safe paths or might as well be steep, exposed trails and thus even more dangerous than the via ferrata itself. So take that into account as well!