4-2-3-1 is not "a defensive formation". No formation is. It's about how it's applied. You can have a ridiculously attacking 4-2-3-1 or a rigid, defensive 4-3-3. I don't even think our application of the system is particularly defensive.
Having said that, we need to have some degree of defensiveness to make up for our piss poor options there. We need to have at least one player shielding the two center backs, and it then follows that we should have one player alongside him to link the defensively minded midfielders with the more attacking ones. So the 2 part in the formation is valid. We're also quite well served with attacking midfielders, so makes sense to put 3 of them there. 2 up front is dead, so it's going to be 1. So...4-2-3-1.
While I would like to see us try a similar system to what the OP said, I'm not convinced the answer to playing 2 poor central defenders is to play 3. Especially if we're telling the full backs to attack more. If we come up against any team that plays advanced wingers, then one of two things will happen. Either our full backs will get pegged back relentlessly and turn it into a 5 at the back (one less player getting forward) or the center backs have to come out. The thought of someone like Grant Hanley lumbering out to take on a rampaging winger gives me the fear.
So the problem isn't that 4-2-3-1 is used. It isn't even that it's always used. It's the application of it, and a lot of the time it's some players putting in absolutely dreadful performances that undermine any system the manager puts in place.