"Fronting," as opposed to "net-side positioning," is a lot more common as a defensive strategy now than it used to be across the league.
There's a number of reasons for that. Goalies are bigger and generally better at aggressively pressing angles than they used to be, which means they can rely on "positional" saves instead of seeing and reacting to the puck cleanly, which in turn devalues clearing their shooting lanes.
There's also been a lot of research into the value of getting the puck to the net in recent years (and thus the value of preventing that from happening), and it's easier to prevent that as a defender when you're fronting since you can more easily fill and press out into shooting lanes. Fewer pucks to the net means fewer saves needed, and fewer rebounds to contest. Fronting also makes it more difficult for the opposing forward near the net to get a clean deflection on an incoming puck since it's going through another person before it gets to him.
It's also easier for a fronting defenseman to close down lateral passing lanes, which are always dangerous, and to defend the "space" you are responsible for in general when you're not crammed between an opponent and your goalie right in front of the net. A defender maintaining net-side positioning is essentially fighting through a pick anytime he wants to do anything beyond engage with that forward immediately in front of him.
A fronting defenseman is much more likely to generate a turnover or change in possession than a net-side one, which fuels transition play. On top of that, it can lead to easy zone clears when the defense wins the puck, and even odd man breaks, since the forward who was being fronted is now trapped behind the play after the possession change.
The rule enforcement changes in recent years that have generally made it more difficult to manhandle and punish opponents who camp in front of the net is also a factor, as that makes it more difficult effectively nullify an opponent when you're engaged from a net-side position.
Since the Blues have a fairly mobile and offensively talented defensive corps, it makes a lot of sense to have them "front" as it plays to their strengths and generally avoids their weaknesses (asking them to engage in and win pitched physical battles in front of the net where their mobility, active sticks, etc. are generally non-factors).
Of course, there are downsides to not playing net-side defense. If a puck does make it through, the defender is now at a disadvantage when contesting a rebound. If your goalies isn't good at controlling rebounds, that can be a significant problem. The defender gets to camp in front of your goalie relatively uncontested, and if your goalie isn't adept at peeking around him, or if he struggles with positional saves in general, those can also be problems.
It's always a trade-off for stuff like this. In general, I think the Blues are better off fronting from a system and personnel standpoint. Unfortunately, the goaltending issues behind them currently can exacerbate the drawbacks of that approach, but if Allen is struggling with his fundamentals/positioning, it's not like playing a different system is going to negate that. Making the team less effective around him isn't a viable solution. Allen has just got to player better, or the Blues need to find someone else who is a better fit for what they're trying to do here.
I completely understand the advantages of "fronting" your assignment, and how it is particularly effective in today's NHL. It wasn't widely used as a tactic back when I played defense, but back then we had the benefit of being able to behead our opponents. 
. I can see fronting as being particularly effective for defenseman like Pietrangelo, Dunn, Shattenkirk, etc, who have the IQ and soft hands to effectively employ it. I wonder however, if players like Edmundson or Bortuzzo might be more effective using net-side positioning. At least, sometimes. I have noticed that Colton Parayko loves to front his man. (I rarely see him do anything else!) I cannot help but wonder if he would also be more effective at net-side defending, as he has the size, weight, and most importantly, lateral mobility, to neutralize his opponent.
